STAT 613 - 统计代写答疑辅导

标签： STAT 613

统计代写|回归分析作业代写Regression Analysis代考| Interpreting an ESF and its parameter estimates

Posted on 2022年4月25日2022年4月25日 by statistics-lab

如果你也在怎样代写回归分析Regression Analysis这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

回归分析是一种强大的统计方法，允许你检查两个或多个感兴趣的变量之间的关系。虽然有许多类型的回归分析，但它们的核心都是考察一个或多个自变量对因变量的影响。

statistics-lab™ 为您的留学生涯保驾护航在代写回归分析Regression Analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写回归分析Regression Analysis代写方面经验极为丰富，各种代写回归分析Regression Analysis相关的作业也就用不着说。

我们提供的回归分析Regression Analysis及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|回归分析作业代写Regression Analysis代考| Interpreting an ESF and its parameter estimates

统计代写|回归分析作业代写Regression Analysis代考|Comparisons between ESF and SAR model specification

The simplest version of MESF accounts for $\mathrm{SA}$ by including a nonconstant mean in a regression model. The spatial SAR specification does this as well by including the term $\left[(1-\rho) \beta_{0} 1+\rho \mathbf{W Y}\right]$, where $\beta_{0}$ denotes the intercept term. The pure SA SAR model is specified as
$$
\mathbf{Y}=(1-\rho) \beta_{0} 1+\rho \mathbf{W}+\boldsymbol{\varepsilon},
$$
employing the row-standardized version of matrix $\mathbf{C}$, namely, matrix $\mathbf{W}$. For the Box-Cox transformed PD studied in this chapter, the maximum likelihood estimate of the SA parameter is $\hat{\rho}=0.70120$. This $\mathrm{SA}$ term

accounts for about $48.1 \%$ of the variance in the Box-Cox transformed PD across Texas. This percentage is less than the $62 \%$ for the ESF specification, in part because the SAR specification includes all, not only the relevant subset of, eigenvectors, introducing some noise into its estimation. Meanwhile, the SAR residual Shapiro-Wilk statistic, $0.96204$, is statistically significant $(p<0.0001)$. Both Getis and Griffith $(2002)$ and Thayn and Simanis (2013) present comparisons of spatial autoregressive and ESF analyses. An ESF specification frequently outperforms a spatial autoregressive specification.
Perhaps one of the greatest advantages MESF has vis-à-vis spatial autoregression is its ability to visualize the SA latent in a georeferenced attribute variable. It also has implementation advantages for generalized linear models (GLMs; see Chapter 5 ).

统计代写|回归分析作业代写Regression Analysis代考|Simulation experiments based upon ESFs

Griffith (2017) argues that MESF is superior to spatial autoregression for spatial statistical simulation experiments because it preserves an underlying map pattern and is characterized by constant variance; in other words, it supports conditional geospatial simulations. A spatial analyst can undertake a simulation experiment employing MESF in one of the following three ways: (1) draw a random error term from a normal distribution with mean zero and variance equal to the linear regression mean squared error; (2) randomly permute the n residuals calculated with linear regression estimation; and, (3) randomly sample, with replacement, the n residuals from the linear regression estimation (similar to bootstrapping). Each of these three strategies was used to perform a sensitivity analysis simulation for the ESF constructed in Section 3.2.2. Each simulation experiment involved 10,000 replications (to profit from the Law of Large Numbers).

The first simulation experiment added random noise $\varepsilon_{i} \sim \mathrm{N}\left(0,1.24350^{2}\right)$, $\mathrm{i}=1,2, \ldots, 254$, to the ESF + intercept tern (i.e., $4.40986$ ). The simulation mean of the map averages (based upon sets of $254 \varepsilon_{i}$ ) is $-0.00045$; the simulation mean of the map variances is $1.15826$. Fig. $3.5 \mathrm{~A}$ portrays the simulated mean map pattern for the simulated log-transformed PD values; it essentially is identical to the map pattern in Fig. 3.1B. The variances for the individual county simulations span the range from $1.13704^{2}$ to $1.18137^{2}$; the F-ratio for these two extreme variances is $1.08$, which is not statistically significant, yielding a single variance class (Fig. 3.5B). One important advantage of MESF vis-à-vis spatial autoregression-based simulation experiments is that the variance is constant across a geographic landscape, which is not the case

for spatial autoregression (see Griffith, 2017). The simulation mean $\mathrm{R}^{2}$ value is $0.6699$, which is somewhat greater than the actual $\mathrm{R}^{2}$ value. Meanwhile, the simulation mean Shapiro-Wilk probability is $0.50136 .$

Table $3.1$ tabulates the eigenvector selection significance level probabilities, Psig, as well as the eigenvector selection simulation probabilities, psimUsing a $10 \%$ level of significance selection criterion renders roughly a $10 \%$ chance that some of the 52 eigenvectors not selected in the original analysis are selected in a simulation analysis. The relationship between these two selection probabilities may be described as follows:
$$
0.24\left(\mathrm{c}^{-3.35 p_{u}^{2.2}}-\mathrm{e}^{-3.35}\right), \mathrm{pscudo}^{-\mathrm{R}^{2}} \approx 1.0000
$$

统计代写|回归分析作业代写Regression Analysis代考|ESF prediction with linear regression

Prediction is a valuable use of linear regression and is alluded to by the PRESS statistic. Redundant attribute information (i.e., multicollinearity) with the covariates supports the prediction of the response variable; each of these predictions is a conditional mean (i.e., a regression fitted value) based upon the given covariates used to compute it. An extension of this prediction capability is to observations not included in the original sample; a set of estimated regression coefficients enables the calculation of a prediction with covariates measured for out-of-sample observations. These supplemental observations have an additional source of variation affiliated with them, namely, their own stochastic noise, which is not addressed during estimation of the already-calculated regression coefficients.

Cross-validation offers an application of ESF prediction with linear regression. This prediction may be executed with the following modified pure SA linear regression specification when a single attribute variable value, $y_{\mathrm{m}}$, is miscing
$$
\left(\begin{array}{c}
\mathbf{Y}{\mathrm{o}} \ 0 \end{array}\right)=\beta{0} \mathbf{1}-\mathrm{y}{\mathrm{m}}\left(\begin{array}{c} \mathbf{0}{\mathrm{o}} \
1
\end{array}\right)+\sum_{\mathrm{k}=1}^{\mathrm{K}}\left(\begin{array}{c}
\mathbf{E}{\mathrm{o}, \mathrm{k}} \ \mathbf{E}{\mathrm{m}, \mathrm{k}}
\end{array}\right) \boldsymbol{\beta}{\mathrm{E}{\mathrm{K}}}+\left(\begin{array}{c}
\boldsymbol{\varepsilon}_{\mathrm{o}} \
0
\end{array}\right),
$$
where the subscript o denotes observed data, the subscript $m$ denotes missing data, and 0 is a vector of zeros. This specification subtracts the unknown data

values, $y_{\mathrm{m}}$, from both sides of the equation and then allows these values to be estimated as regression parameters (i.e., conditional means). In doing so, these conditional means are equivalent to their fitted values and hence have residuals of zero.

Fig. $3.7$ portrays the scatterplot of the log-transformed 2010 Texas PD (vertical axis) versus the corresponding 254 imputed values calculated with Eq. (3.8) but with no covariates (i.e., a pure SA specification); this exercise is similar to kriging. The linear regression equation describing this correspondence may be written as follows:
$$
\hat{\mathrm{Y}}=0.98849+0.77990 \mathrm{Y}_{\text {predicted }}, \mathrm{R}^{2}=0.4078
$$

回归分析代写

统计代写|回归分析作业代写Regression Analysis代考|Comparisons between ESF and SAR model specification

最简单的 MESF 版本小号一种通过在回归模型中包含非常量均值。空间 SAR 规范也通过包含术语来做到这一点[(1−ρ)b01+ρ在是]，在哪里b0表示截距项。纯 SA SAR 模型指定为
是=(1−ρ)b01+ρ在+e,
使用矩阵的行标准化版本C，即矩阵在. 对于本章研究的 Box-Cox 变换的 PD，SA 参数的最大似然估计为ρ^=0.70120. 这小号一种学期

约占48.1%德克萨斯州 Box-Cox 转换 PD 的方差。这个百分比低于62%对于 ESF 规范，部分原因是 SAR 规范不仅包括特征向量的相关子集，还包括所有特征向量，在其估计中引入了一些噪声。同时，SAR 残差 Shapiro-Wilk 统计量，0.96204, 具有统计学意义(p<0.0001). 盖蒂斯和格里菲斯(2002)Thayn 和 Simanis (2013) 比较了空间自回归和 ESF 分析。ESF 规范经常优于空间自回归规范。
MESF 相对于空间自回归的最大优势之一可能是它能够可视化地理参考属性变量中潜在的 SA。它还具有广义线性模型（GLM；见第 5 章）的实施优势。

统计代写|回归分析作业代写Regression Analysis代考|Simulation experiments based upon ESFs

Griffith (2017) 认为，MESF 在空间统计模拟实验中优于空间自回归，因为它保留了基础地图模式并且具有恒定方差的特点；换句话说，它支持有条件的地理空间模拟。空间分析师可以通过以下三种方式之一使用 MESF 进行模拟实验： (1) 从均值为零且方差等于线性回归均方误差的正态分布中绘制随机误差项；(2) 随机排列用线性回归估计计算的n个残差；(3) 随机抽取线性回归估计的 n 个残差进行替换（类似于自举）。这三种策略中的每一种都用于对第 3.2.2 节中构建的 ESF 进行敏感性分析模拟。

第一个模拟实验添加了随机噪声e一世∼ñ(0,1.243502), 一世=1,2,…,254, 到 ESF + 截取 tern（即，4.40986）。地图平均值的模拟平均值（基于254e一世）是−0.00045; 地图方差的模拟平均值为1.15826. 如图。3.5 一种描绘模拟对数转换 PD 值的模拟平均图模式；它本质上与图 3.1B 中的地图模式相同。各个县模拟的方差范围从1.137042到1.181372; 这两个极端方差的 F 比是1.08，这在统计上不显着，产生一个单一的方差类（图 3.5B）。MESF 相对于基于空间自回归的模拟实验的一个重要优势是，在整个地理景观中，方差是恒定的，但事实并非如此

用于空间自回归（参见 Griffith，2017）。模拟平均值R2值为0.6699，这比实际的要大一些R2价值。同时，模拟平均夏皮罗-威尔克概率为0.50136.

桌子3.1将特征向量选择显着性水平概率 Psig 以及特征向量选择模拟概率 psimUsing a10%显着性水平选择标准大致呈现10%有可能在模拟分析中选择了原始分析中未选择的 52 个特征向量中的一些。这两个选择概率之间的关系可以描述如下：
0.24(C−3.35p在2.2−和−3.35),psC在d这−R2≈1.0000

统计代写|回归分析作业代写Regression Analysis代考|ESF prediction with linear regression

预测是线性回归的一种有价值的用途，并由 PRESS 统计量提及。带有协变量的冗余属性信息（即多重共线性）支持响应变量的预测；这些预测中的每一个都是基于用于计算它的给定协变量的条件平均值（即回归拟合值）。这种预测能力的扩展是原始样本中未包含的观察结果；一组估计的回归系数可以使用针对样本外观察测量的协变量来计算预测。这些补充观察具有与它们相关的额外变化源，即它们自己的随机噪声，在估计已经计算的回归系数期间没有解决。

交叉验证提供了 ESF 预测与线性回归的应用。当单个属性变量值时，可以使用以下修改后的纯 SA 线性回归规范执行该预测，是米, 是错配
(是这 0)=b01−是米(0这 1)+∑ķ=1ķ(和这,ķ 和米,ķ)b和ķ+(e这 0),
其中下标 o 表示观测数据，下标米表示缺失数据，0 是零向量。本规范减去未知数据

价值观，是米，从等式的两侧，然后允许将这些值估计为回归参数（即条件均值）。这样做时，这些条件均值等于它们的拟合值，因此残差为零。

如图。3.7描绘了对数转换的 2010 年德克萨斯州 PD（垂直轴）与使用方程式计算的相应 254 个估算值的散点图。(3.8) 但没有协变量（即纯 SA 规范）；这个练习类似于克里金法。描述这种对应关系的线性回归方程可以写成如下：
是^=0.98849+0.77990是预料到的 ,R2=0.4078

统计代写|回归分析作业代写Regression Analysis代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

随机过程代考

在概率论概念中，随机过程是随机变量的集合。若一随机系统的样本点是随机函数，则称此函数为样本函数，这一随机系统全部样本函数的集合是一个随机过程。实际应用中，样本函数的一般定义在时间域或者空间域。 随机过程的实例如股票和汇率的波动、语音信号、视频信号、体温的变化，随机运动如布朗运动、随机徘徊等等。

贝叶斯方法代考

贝叶斯统计概念及数据分析表示使用概率陈述回答有关未知参数的研究问题以及统计范式。后验分布包括关于参数的先验分布，和基于观测数据提供关于参数的信息似然模型。根据选择的先验分布和似然模型，后验分布可以解析或近似，例如，马尔科夫链蒙特卡罗 (MCMC) 方法之一。贝叶斯统计概念及数据分析使用后验分布来形成模型参数的各种摘要，包括点估计，如后验平均值、中位数、百分位数和称为可信区间的区间估计。此外，所有关于模型参数的统计检验都可以表示为基于估计后验分布的概率报表。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

机器学习代写

随着AI的大潮到来，Machine Learning逐渐成为一个新的学习热点。同时与传统CS相比，Machine Learning在其他领域也有着广泛的应用，因此这门学科成为不仅折磨CS专业同学的“小恶魔”，也是折磨生物、化学、统计等其他学科留学生的“大魔王”。学习Machine learning的一大绊脚石在于使用语言众多，跨学科范围广，所以学习起来尤其困难。但是不管你在学习Machine Learning时遇到任何难题，StudyGate专业导师团队都能为你轻松解决。

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。

回归分析代写

多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习和应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|回归分析作业代写Regression Analysis代考| Estimating an ESF as an OLS problem

Posted on 2022年4月25日2022年4月25日 by statistics-lab

如果你也在怎样代写回归分析Regression Analysis这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的回归分析Regression Analysis及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|回归分析作业代写Regression Analysis代考| Estimating an ESF as an OLS problem

统计代写|回归分析作业代写Regression Analysis代考|An illustrative linear regression example

A pure SA analysis ignores covariates and estimates the SA latent in an attribute variable map pattern. This type of analysis is pertinent to, for example, the construction of histograms for georeferenced RVs or the calculation of Pearson product moment correlation coefficients for pairs of georeferenced RVs, among other things. The MESF linear regression equation, which assumes normally distributed residuals, is the following nonconstant mean-only specification:
$$
\mathbf{Y}=\mathbf{1} \boldsymbol{\beta}{0}+\mathrm{E}{\mathrm{K}} \boldsymbol{\beta}_{\mathrm{E}}+\boldsymbol{\xi} .
$$
One traditional specification error concern here pertains to how closely the response variable Y conforms to a normal distribution. Analysts frequently subject a nonnormal set of attribute values to a $B o x-\operatorname{Cox} /$ Manly transformation to normality (see Griffith, 2013).

Consider the 2010 population density (PD) across the 254 counties of Texas (see Fig. 3.1A); urban areas are conspicuous in this map pattern, revealing geographic heterogeneity. Raw PD values do not conform closely to a bell-shaped curve (Fig. 3.2A), whereas Box-Cox transformed values LN $(\mathrm{PD}-0.08)$ do (Fig. 3.2B), where LN denotes natural logarithm.

统计代写|回归分析作业代写Regression Analysis代考|The selection of eigenvectors to construct an ESF

The first step in constructing an ESF for the 2010 Texas PD by county is to extract the 254 eigenvectors from the modified SWM $\left(\mathbf{I}-11^{\mathrm{T}} / 254\right) \times$ $\mathbf{C}\left(\mathbf{I}-11^{\mathrm{T}} / 254\right)$, where $0-1$ matrix $\mathrm{C}$ denotes the Texas county SWM, based upon the rook definition of adjacency (see Preface, Fig. P1). Because this PD exhibits PSA, determining an appropriate candidate set of eigenvectors for stepwise regression can begin by setting aside the $149 \mathrm{NSA}$ eigenvectors plus the single eigenvector having a zero eigenvalue (corresponding to the eigenvector proportional to the vector 1 ), which a regression equation already includes for its intercept term. The next step is to determine how many of the 104 PSA eigenvectors to include, counting this number from the largest eigenvalue (i.e., the maximum possible PSA). Chun et al. (2016, p. 75) furnish the following equation to help with this decision:
$$
1+\exp \left{2.1480-\frac{6.1808\left(\mathrm{z}{\mathrm{MC}}+0.6\right)^{0.1742}}{\mathrm{n}{\text {pos }}^{0.1298}}+\frac{3.3534}{\left(\mathrm{z}{\mathrm{MC}}+0.6\right)^{0.1742}}\right} $$ with $\mathrm{n}{\mathrm{Pos}}=104$ (the number of PSA eigenvectors), and $\mathrm{z}{\mathrm{MC}}=13.52$ (the linear regression residuals $z$-score measure of SA) here. This expression indicates that the candidate set should contain the 78 eigenvectors with the largest eigenvalues. Spatial regression analysis using eigenvector spatial filtering One useful criterion for eigenvector selection from the candidate set is the level of significance for each eigenvector’s regression coefficient, which essentially maximizes the linear regression $\mathrm{R}^{2}$ value; other selection criteria could be utilized (see Griffith, 2004). In addition, a stepwise procedure that combines both forward selection and backward elimination supports the construction of a parsimonious ESF. Because the eigenvectors are mutually orthogonal and uncorrelated, the primary factor in eigenvector selection during any given step is the marginal error sum of squares for that step. Of the 78 candidate eigenvectors, 26 were selected using a significance level criterion of $0.10$, accounting for roughly $62.5 \%$ of the variation in logtransformed PD across the counties of Texas (Fig. 3.1B), highlighting the Dallas, Houston, and Austin-San Antonio metropolitan regions and indicating that $\mathrm{SA}$ introduces variance inflation by more than doubling the underlying IID variance. Table $3.1$ summarizes the stepwise selection results, revealing that global (e.g., $\mathbf{E}{2}$ ), regional (e.g., $\mathbf{E}{19}$ ), and local (e.g., $\mathbf{E}{77}$ ) map pattern ${ }^{1}$ components account for the $\mathrm{SA}$ under study and that the Aegree of SA does not determine the selection sequence.

统计代写|回归分析作业代写Regression Analysis代考|Selected criteria for assessing regression models

Once an ESF is constructed, model dingnostics should be performed. The predicted residual error sum of squares (PRESS) statistic is a useful global diagnostic to calculate because it relates to a cross-validation assessment, with the set of covariates being held constant. Values of the ratio PRESS/ESS close to 1, where ESS denotes error sum of squares, indicate good model performance in this context because the corresponding estimated model fitting and prediction error essentially are the same (i.e., the estimated trend line also describes new observations well). Here this values is $376.737 / 355.645=1.059$, implying a very respectable model performance with regard to the cross-validation criterion.

Three features of the linear regression residuals merit assessment. The first concerns normality (Fig. 3.3A); here the Shapiro-Wilk statistic for the linear regrension residuals is $0.98030(p=0.0014)$; the frequency distribution for these residuals differs statistically, but not substantively, from a bell-shaped curve. The second concerns residual SA. The expected value
‘The grouping into global, regional, and local map patterns is subjective. These terms, respectively, refer to $\mathrm{MC} / \mathrm{MC}_{\max }$ (i-e., the maximum $\mathrm{MC}$ ) values in the ranges $0.9-1,0.7-0.9$, and $0.25-0.7$. The maximum MC value here is $1.09798$, which should be used to standardize $\mathrm{MC}$ values to make them comparable across geoggraphic handscapes.

回归分析代写

统计代写|回归分析作业代写Regression Analysis代考|An illustrative linear regression example

纯 SA 分析忽略协变量并估计属性变量映射模式中的潜在 SA。例如，这种类型的分析与地理参考 RV 直方图的构建或地理参考 RV 对的 Pearson 积矩相关系数的计算等有关。假设正态分布残差的 MESF 线性回归方程是以下非常量仅均值规范：
$$
\mathbf{Y}=\mathbf{1} \boldsymbol{\beta} {0}+\mathrm{E} { \mathrm{K}} \boldsymbol{\beta}_{\mathrm{E}}+\boldsymbol{\xi} 。
$$
这里一个传统的规范误差关注点与响应变量 Y 与正态分布的符合程度有关。分析师经常将一组非正态属性值置于乙这X−考克斯⁡/向常态的男子气概转变（参见 Griffith，2013 年）。

考虑 2010 年德克萨斯州 254 个县的人口密度（PD）（见图 3.1A）；城市地区在该地图图案中非常显眼，显示出地理异质性。原始 PD 值不符合钟形曲线（图 3.2A），而 Box-Cox 转换值 LN(磷D−0.08)do（图 3.2B），其中 LN 表示自然对数。

统计代写|回归分析作业代写Regression Analysis代考|The selection of eigenvectors to construct an ESF

按县为 2010 年德克萨斯州 PD 构建 ESF 的第一步是从修改后的 SWM 中提取 254 个特征向量(一世−11吨/254)× C(一世−11吨/254)，在哪里0−1矩阵C表示得克萨斯县 SWM，基于邻接的 rook 定义（参见前言，图 P1）。由于此 PD 表现出 PSA，因此可以先将149ñ小号一种特征向量加上具有零特征值的单个特征向量（对应于与向量 1 成比例的特征向量），回归方程已经包括其截距项。下一步是确定要包括多少 104 个 PSA 特征向量，从最大特征值（即最大可能的 PSA）开始计算这个数字。春等人。(2016, p. 75) 提供以下等式来帮助做出这一决定：
1+\exp \left{2.1480-\frac{6.1808\left(\mathrm{z}{\mathrm{MC}}+0.6\right)^{0.1742}}{\mathrm{n}{\text {pos } }^{0.1298}}+\frac{3.3534}{\left(\mathrm{z}{\mathrm{MC}}+0.6\right)^{0.1742}}\right}1+\exp \left{2.1480-\frac{6.1808\left(\mathrm{z}{\mathrm{MC}}+0.6\right)^{0.1742}}{\mathrm{n}{\text {pos } }^{0.1298}}+\frac{3.3534}{\left(\mathrm{z}{\mathrm{MC}}+0.6\right)^{0.1742}}\right}和n磷这s=104（PSA特征向量的数量），和和米C=13.52（线性回归残差和-SA 的得分度量）在这里。这个表达式表明候选集应该包含 78 个特征向量的最大特征值。使用特征向量空间滤波的空间回归分析从候选集中选择特征向量的一个有用标准是每个特征向量的回归系数的显着性水平，它基本上使线性回归最大化R2价值; 可以使用其他选择标准（参见 Griffith，2004 年）。此外，结合前向选择和后向消除的逐步过程支持简约 ESF 的构建。因为特征向量是相互正交且不相关的，所以在任何给定步骤中选择特征向量的主要因素是该步骤的边际误差平方和。在 78 个候选特征向量中，使用显着性水平标准选择了 26 个0.10, 大致占62.5%得克萨斯州各县的对数转换 PD 的变化（图 3.1B），突出显示达拉斯、休斯顿和奥斯汀-圣安东尼奥大都市区，并表明小号一种通过将基础 IID 方差增加一倍以上来引入方差膨胀。桌子3.1总结了逐步选择的结果，揭示了全局（例如，和2), 地区性的 (例如,和19）和本地（例如，和77) 地图图案1组件占小号一种正在研究中，并且 SA 的 Aegree 不能确定选择顺序。

统计代写|回归分析作业代写Regression Analysis代考|Selected criteria for assessing regression models

构建 ESF 后，应执行模型诊断。预测残差平方和 (PRESS) 统计量是一种有用的全局诊断计算，因为它与交叉验证评估相关，协变量集保持不变。PRESS/ESS 比值接近 1，其中 ESS 表示误差平方和，表明在这种情况下模型性能良好，因为相应的估计模型拟合和预测误差基本相同（即，估计的趋势线也描述了新的观察结果好）。这里的值是376.737/355.645=1.059，这意味着关于交叉验证标准的模型性能非常可观。

线性回归残差的三个特征值得评估。第一个涉及常态（图 3.3A）；这里线性回归残差的 Shapiro-Wilk 统计量是0.98030(p=0.0014); 这些残差的频率分布在统计上与钟形曲线不同，但没有实质性差异。第二个涉及剩余 SA。期望值
‘对全球、区域和本地地图模式的分组是主观的。这些术语分别指米C/米C最大限度（即，最大米C) 范围内的值0.9−1,0.7−0.9，和0.25−0.7. 这里的最大 MC 值为1.09798, 这应该用于标准化米C值以使它们在地理景观中具有可比性。

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统计代写|回归分析作业代写Regression Analysis代考|MESF and linear regression

Posted on 2022年4月25日2022年4月25日 by statistics-lab

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统计代写|回归分析作业代写Regression Analysis代考|MESF and linear regression

统计代写|回归分析作业代写Regression Analysis代考|A theoretical foundation for ESFs

The theoretical foundation for MESF contains two components, one derivable from the general spatial autoregressive model specification and the other derivable from the concept of a random effects term.

The spatial autoregressive response (AR) model (known as the spatial lag model in spatial econometrics) specification, an auto-normal model, may be written as follows, using the spatial linear operator $(\mathbf{I}-\rho \mathbf{C})$ and matrix notation:
$$
\mathbf{Y}=(\mathbf{I}-\rho \mathbf{C})^{-1}\left(\mathbf{X} \boldsymbol{\beta}{\mathbf{X}}+\boldsymbol{\varepsilon}\right) $$ where $\boldsymbol{\beta}{\mathbf{X}}$ is a $(\mathrm{p}+1)$-by-1 vector of regression coefficients for $\mathrm{p}$ covariates and the intercept term, $\rho$ is the SA parameter, and $\varepsilon$ is an n-by-1 vector of independent and identically discributed (IID) normal random variables (RVs) with mean zero and constant variance $\sigma^{2}$. The standard maximum likelihood estimation of parameters in Eq. (3.2) involves it being rewritten as the following nonlinear regression specification:

$$
(\mathbf{I}-\rho \mathbf{C}) \mathbf{Y}=(\mathbf{I}-\rho \mathbf{C})(\mathbf{I}-\rho \mathbf{C})^{-1}\left(\mathbf{X} \boldsymbol{\beta}{\mathbf{X}}+\boldsymbol{\varepsilon}\right) \Rightarrow \mathbf{Y}=\rho \mathbf{C Y}+\mathbf{X} \boldsymbol{\beta}{\mathbf{X}}+\boldsymbol{\varepsilon}
$$
The eigenfunction decomposition of the $S W M C$ is $\mathbf{E} \Lambda \mathbf{E}^{\mathrm{T}}$, where matrix $\mathbf{E}$ is the set of $n$ eigenvectors of SWM $\mathrm{C}$, diagonal matrix $\boldsymbol{\Lambda}$ contains the set of $\mathrm{n}$ eigenvalues of SWM C, with the ordering of entries in these two matrices being the same eigenfunctions, and superscript $T$ denotes the matrix transpose operation. Substituting this decomposition of SWM C into Eq. (3.3) produces.
$$
\mathbf{Y}=\rho \mathbf{E} \boldsymbol{A} \mathbf{E}^{\mathrm{T}} \mathbf{Y}+\mathbf{X} \boldsymbol{\beta}{\mathbf{X}}+\boldsymbol{\varepsilon}, $$ where $\mathbf{E}^{\mathrm{T}} \mathbf{Y}$ is the ordinary least squares (OLS) estimate of regression coefficients when response variable $\mathbf{Y}$ is regressed on eigenvector matrix $\mathbf{E}$. A stepwise selection procedure (e.g., simultaneous forward-backward) eliminates $j$ eigenvectors for which $\mathbf{E}{j}^{\mathrm{T}} \mathbf{Y} \approx 0$ (i.e., the $\mathrm{SA}$ map patterns for these eigenvectors do not account for any SA in the regression residuals) or for which $\rho \lambda_{j} \approx 0$ (i.e., the map pattern displays a trivial degree of SA), which in practice tends to be a large majority of the eigenvectors, leaving $\mathrm{K}<<\mathrm{n}$ eigenvectors in the model specification:
$$
\mathbf{Y}=\mathbf{E}{\mathrm{K}} \boldsymbol{\beta}{\mathrm{E}}+\mathbf{X} \boldsymbol{\beta}_{\mathrm{X}}+\boldsymbol{\xi},
$$

统计代写|回归分析作业代写Regression Analysis代考|The fundamental theorem of MESF

A statement of the fundamental theorem of MESF appears in Section 2.1.3. It is based upon several theorems in matrix algebra, including the fundarnental theorem of principal components analysis (see Tatsuoka, 1988, p. 146), which may be translated as follows:
Given a modified $n-b y-n S W M\left(I-11^{T} / n\right) C\left(I-11^{T} / n\right)$ for a given geographic land scape, we can derive a set of orthogonal and uncorrelated variables $\boldsymbol{E}{\imath}, \boldsymbol{E}{2}, \ldots, \boldsymbol{E}{n}$ by a set of linear transformations corresponding to the principal-axes rotation [i.e, the rigid rotation whose transformation matrix $E$ has the n eigervectors of matrix $\left.\left(I-11^{\top} / n\right) C\left(I-11^{T} / n\right)\right]$ as its columns. The $S A$ measures of this new set of variables are given by the diagonal matrix $\left.\left(|^{\top} \mathrm{C}\right]\right) \Lambda=\left[n / \mathbf{1}^{\top} C 1 \mathbf{E}^{\top}\left(I-11^{\top} / n\right)\right.$ $C\left(I-11^{\top} / n\right) E$, whose diagonal elements are the n MCs of the corresponding map patterns produced by the n eigenvectors of matrix $\boldsymbol{E}$. Orthogonality results from the matrix $\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathrm{C}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right)$ being symmetric (if $\mathbf{C}$ is a symmetric matrix, then $\mathbf{A C A}{ }^{T}$ is a symmetric matrix). Uncorrelatedness results from the pre- and postmultiplication of matrix $\mathbf{C}$ by the projection matrix $\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right)$, resulting in a single eigenvector proportional to the $n-b y-1$ vector 1 , and hence the $n-1$ other eigenvectors having elements that sum to zero; the numerator of the Pearson product moment correlation coefficient for a pair of different eigenvectors has a cross-product term (e.g., XY) of zero (orthogonality) and a product of two means (each being a sum of the elements of an eigenvector, with at least one of these sums equal to zero) of zero (Griffith $2000 \mathrm{~b}, \mathrm{p} .105$ ). Tiefelsdorf and Boots (1995; Section 2.1.2) prove that the MC for a given eigenvector $\mathbf{E}{j}$ is given by $\left(\mathrm{n} / \mathbf{1}^{\mathrm{T}} \mathrm{C} 1\right) \lambda_{\mathrm{j}}$. The rank ordering of the $\mathrm{R}$ ayleigh quotients
$$
\left(n / 1^{\mathrm{T}} \mathrm{C} 1\right) \mathbf{E}^{\mathrm{T}}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathrm{C}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathbf{E} /\left(\mathbf{E}^{\mathrm{T}} \mathbf{E}\right)=\left(\mathrm{n} / \mathbf{1}^{\mathrm{T}} \mathrm{C} 1\right) \boldsymbol{\Lambda}
$$
produces the sequential ordering from the maximum possible level of positive SA (PSA) to the maximum possible level of negative SA (NSA; see de Jong, Sprenger, \& van Veen, 1984).

Because one eigenvector element corresponds to each of the $\mathrm{n}$ areal units in a geographic landscape, a map can portray the geographic distribution of each set of eigenvector elements. Consequently, a map of the $\mathrm{ESF}{\mathbf{K}} \boldsymbol{\beta}{\mathbf{E}}$ fumishes a visualization of SA; as such, it supplements the Moran scatterplot graphic tool. Furthermore, because each eigenvector is an n-by-1 variate, eigenvectors can be treated like covariates and included in a linear regression analysis.

统计代写|回归分析作业代写Regression Analysis代考|Map pattern and SA: Heterogeneity in map-wide trends

SA may be interpreted in a number of different ways, one of which is map pattern (Griffith, 1992). Pattern refers to some discernible real-world regularity that contains elements recurring in a predictable manner. Map pattern refers to this regularity and repetitiveness occurring in two dimensions and is the basis for spatial interpolation (prediction linking to kriging in geostatistics). SA makes map pattern possible by organizing attribute values on a map in such a way that for PSA, for example, relatively high values cluster together in a geographic landscape, as do relatively intermediate, and relatively low, values. This geographic organization can yield global gradients across, as well as large regional or small local clusters in, a geographic landscape; in general, neighborhood subsets of georeferenced attribute values are similar or dissimilar (NSA). These are the components of map pattern depicted by the modified SWM eigenvectors with, respectively, large, moderate, or small but not close to zero, eigenvalues. In other words, map pattern has to do with the geographic arrangement of attribute values of a map, with the nature and degree of (dis)similarities of nearby values relating to $\mathrm{SA}$.
Heterogeneity refers to a collection of diverse elements, elements that are nonuniform in the composition of their attribute values. In terms of statistical properties, these elements are not IID (see Section 3.1). In classical linear regression, a response variable $Y$ often is considered heterogeneous in its individual observation means, resulting in the term $\mathbf{X} \boldsymbol{\beta}{\mathbf{X}}$ being included in a linear regression specification. This specification strategy seeks to account for heterogeneity with the regression mean, rendering residuals that are IID and hence homogeneous. If $X \equiv 1$, then the mean of $Y$ for each areal unit is the constant $\beta{0}$; this is the special case of a homogeneous $Y$. In the presence of $\mathrm{SA}$, the residuals still have a mean of zero, but now heterogeneity persists through their variances being unequal; this outcome is one consequence of variance inflation by SA. Eq. (3.4) highlights how MESF addresses this problem by replacing the constant mean with a variable mean:
$$
\mathbf{Y}=\mathrm{E}{\mathrm{K}} \boldsymbol{\beta}{\mathrm{E}}+\mathbf{X} \boldsymbol{\beta}{\mathrm{X}}+\boldsymbol{\xi}=\left(\mathbf{1} \boldsymbol{\beta}{0}+\mathrm{E}{\mathrm{K}} \boldsymbol{\beta}{\mathrm{E}}\right)+\mathbf{X}{\mathrm{P}} \boldsymbol{\beta}{\mathrm{X}}+\boldsymbol{\xi}
$$

回归分析代写

统计代写|回归分析作业代写Regression Analysis代考|A theoretical foundation for ESFs

MESF 的理论基础包含两个组成部分，一个来自一般空间自回归模型规范，另一个来自随机效应项的概念。

空间自回归响应 (AR) 模型（在空间计量经济学中称为空间滞后模型）规范，一种自正态模型，可以使用空间线性算子编写如下(一世−ρC)和矩阵表示法：
是=(一世−ρC)−1(XbX+e)在哪里bX是一个(p+1)-by-1 回归系数向量p协变量和截距项，ρ是 SA 参数，并且e是独立同分布 (IID) 正态随机变量 (RV) 的 n×1 向量，均值为零且方差恒定σ2. 方程中参数的标准最大似然估计。(3.2) 涉及将其重写为以下非线性回归规范：(一世−ρC)是=(一世−ρC)(一世−ρC)−1(XbX+e)⇒是=ρC是+XbX+e
的特征函数分解小号在米C是和Λ和吨, 其中矩阵和是集合nSWM 的特征向量C, 对角矩阵Λ包含一组nSWM C 的特征值，这两个矩阵中条目的排序是相同的特征函数，上标吨表示矩阵转置操作。将 SWM C 的这种分解代入方程式。(3.3) 产生。
是=ρ和一种和吨是+XbX+e,在哪里和吨是是响应变量时回归系数的普通最小二乘 (OLS) 估计是在特征向量矩阵上回归和. 逐步选择过程（例如，同时向前向后）消除了j特征向量和j吨是≈0（即，小号一种这些特征向量的映射模式不考虑回归残差中的任何 SA）或ρλj≈0（即，地图模式显示的 SA 程度很小），在实践中往往是特征向量的大部分，留下ķ<<n模型规范中的特征向量：
是=和ķb和+XbX+X,

统计代写|回归分析作业代写Regression Analysis代考|The fundamental theorem of MESF

MESF 基本定理的陈述出现在第 2.1.3 节。它基于矩阵代数中的几个定理，包括主成分分析的基本定理（参见 Tatsuoka, 1988, p. 146），可以翻译如下
：n−b是−n小号在米(一世−11吨/n)C(一世−11吨/n)对于给定的地理景观，我们可以推导出一组正交且不相关的变量和一世,和2,…,和n通过一组对应于主轴旋转的线性变换[即，其变换矩阵的刚性旋转和具有矩阵的 n 个 eigervectors(一世−11⊤/n)C(一世−11吨/n)]作为它的列。这小号一种这组新变量的度量由对角矩阵给出(|⊤C])Λ=[n/1⊤C1和⊤(一世−11⊤/n) C(一世−11⊤/n)和, 其对角元素是矩阵的 n 个特征向量产生的对应地图图案的 n 个 MC和. 矩阵的正交性结果(一世−11吨/n)C(一世−11吨/n)是对称的（如果C是一个对称矩阵，那么一种C一种吨是一个对称矩阵）。矩阵的前乘和后乘导致不相关性C由投影矩阵(一世−11吨/n)，产生一个与n−b是−1向量 1 ，因此n−1其他元素之和为零的特征向量；一对不同特征向量的 Pearson 积矩相关系数的分子具有一个为零的叉积项（例如 XY）（正交性）和两个均值的乘积（每个均值是一个特征向量的元素之和，其中这些总和中至少有一个等于零）的零（格里菲斯2000 b,p.105）。Tiefelsdorf 和 Boots（1995；第 2.1.2 节）证明给定特征向量的 MC和j是（谁）给的(n/1吨C1)λj. 的排名顺序R艾莉商数
(n/1吨C1)和吨(一世−11吨/n)C(一世−11吨/n)和/(和吨和)=(n/1吨C1)Λ
产生从正 SA (PSA) 的最大可能水平到负 SA 的最大可能水平的顺序排序 (NSA；参见 de Jong, Sprenger, \& van Veen, 1984)。

因为一个特征向量元素对应于每个n地理景观中的面积单位，一张地图可以描绘每组特征向量元素的地理分布。因此，一张地图和小号Fķb和完成 SA 的可视化；因此，它补充了 Moran 散点图图形工具。此外，由于每个特征向量都是 n×1 变量，因此可以将特征向量视为协变量并包含在线性回归分析中。

统计代写|回归分析作业代写Regression Analysis代考|Map pattern and SA: Heterogeneity in map-wide trends

SA 可以用多种不同的方式来解释，其中一种是地图模式（Griffith，1992）。模式是指一些可识别的现实世界规律，其中包含以可预测方式重复出现的元素。地图模式是指这种在二维中出现的规律性和重复性，是空间插值（与地质统计学中的克里金法相关的预测）的基础。SA 通过组织地图上的属性值使地图模式成为可能，例如，对于 PSA，相对较高的值在地理景观中聚集在一起，相对中等和相对较低的值也是如此。这种地理组织可以产生跨越地理景观的全球梯度，以及地理景观中的大型区域或小型局部集群；一般来说，地理参考属性值的邻域子集相似或不同 (NSA)。这些是修改后的 SWM 特征向量所描绘的地图图案的组成部分，分别具有大、中等或小但不接近于零的特征值。换句话说，地图模式与地图属性值的地理排列有关，与附近值的性质和（不）相似程度有关小号一种.
异质性是指不同元素的集合，这些元素的属性值组成不均匀。就统计特性而言，这些元素不是独立同分布的（参见第 3.1 节）。在经典线性回归中，响应变量是通常在其个体观察手段中被认为是异质的，导致术语XbX包含在线性回归规范中。该规范策略旨在解释回归均值的异质性，呈现 IID 的残差，因此是同质的。如果X≡1，然后的平均值是对于每个面积单位是常数b0; 这是同质的特例是. 在……的存在下小号一种，残差的均值仍然为零，但现在异质性仍然存在，因为它们的方差不相等；该结果是 SA 方差膨胀的结果之一。方程。(3.4) 强调了 MESF 如何通过用变量均值替换恒定均值来解决此问题：
是=和ķb和+XbX+X=(1b0+和ķb和)+X磷bX+X

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|回归分析作业代写Regression Analysis代考|The spectral analysis of three-dimensional data

Posted on 2022年4月25日2022年4月25日 by statistics-lab

如果你也在怎样代写回归分析Regression Analysis这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的回归分析Regression Analysis及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|回归分析作业代写Regression Analysis代考|The spectral analysis of three-dimensional data

In many cases, the spectral analysis of three-dimensional georeferenced data involves a sequence of maps, one for each point in a specified time series, rather than supplementing planar surfaces with elevation. Griffith and Heurclink (2012) extend the preeeding spectral analysis conceptualizations to this situation. Now the spectral density-based space-time $(\tau, \eta, \nu)-$ lag correlation function becomes, for a regular square tessellation and the rook adjacency definition, and uniformly spaced points in time,
$\frac{\int_{0}^{\pi} \int_{0}^{\pi} \int_{0}^{\pi} \frac{\operatorname{Cos}(\tau \theta) \operatorname{Cos}(\eta \varphi) \operatorname{Cos}(v t)}{\left[1-\operatorname{COS}(t)\left{\rho_{s}[\operatorname{Cos}(\theta)+\operatorname{Cos}(\varphi)]+\rho_{T}\right}\right]^{k}} d \theta d \varphi d t}{\int_{0}^{\pi} \int_{0}^{\pi} \int_{0}^{\pi} \frac{1}{\left[1-\operatorname{COS}(t)\left{\rho_{s}[\operatorname{CoS}(\theta)+\operatorname{CoS}(\varphi)]+\rho_{T}\right}\right]^{k}} \mathrm{~d} \theta \mathrm{d} \varphi \mathrm{dt}}, \boldsymbol{\kappa}=1,2$,
where $t$ denotes the twe argument, $\rho_{\mathrm{s}}$ denotes the SA parameter, and $\rho_{\mathrm{r}}$ denotes the temporal autocorrelation parameter. This specification represents a contemporaneous space-time process, which is additive, whose matrix representation is given by

$$
\mathbf{C}=\mathbf{I}{\mathrm{T}} \otimes \mathbf{I}{\mathrm{s}}-\rho_{\mathrm{s}} \mathbf{C}{\mathrm{T}} \otimes \mathbf{C}{\mathrm{s}}-\rho_{\mathrm{T}} \mathbf{C}{\mathrm{T}} \otimes \mathbf{I}{\mathrm{s}},
$$
where $\otimes$ denotes the Kronecker product mathematical matrix operation, $\mathbf{C}{\mathrm{s}}$ denotes the SWM, $\mathbf{C}{\mathrm{T}}$ denotes the time-series connectivity matrix, $\mathbf{I}{\mathrm{T}}$ denotes the $T$-by-T identify matrix, $\mathbf{I}{s}$ denotes the $\mathrm{n}-\mathrm{by}-\mathrm{n}$ identity matrix, and $1-\operatorname{COS}(\mathrm{t})\left{\rho_{\mathrm{s}}[\operatorname{COS}(\mathrm{u})+\operatorname{COS}(\mathrm{v})]+\rho_{\mathrm{T}}\right}$ are the limiting eigenvalues of the space time connectivity matrix $C$.

An alternative specification is multiplicative and hence describes a space-time lagged process; its matrix representation is given by
$$
\mathbf{C}=\mathbf{I}{\mathrm{T}} \otimes \mathbf{I}{\mathrm{s}}-\rho_{\mathrm{s}} \mathbf{I}{\mathrm{T}} \otimes \mathbf{C}{\mathrm{s}}-\rho_{\mathrm{T}} \mathbf{C}{\mathrm{T}} \otimes \mathbf{I}{\mathrm{s}} \text {, }
$$
and its spectral density-based $(\tau, \eta, \nu)$-lag correlations are given by
For a regular square lattice forming a complete $P-b y-Q$ rectangular region,
$$
\mathbf{C}{\mathrm{s}}=\mathbf{C}{\mathrm{P}} \otimes \mathbf{I}{\mathrm{Q}}+\mathbf{C}{\mathrm{Q}} \otimes \mathbf{I}{\mathrm{r}}, $$ where $C{p}$ and $C_{Q}$, respectively, are $S W M s$ for a $P$ length and a $Q$ length linear landscape, and $\mathbf{I}{\mathrm{P}}$ and $\mathbf{I}{\mathrm{Q}}$, respectively, are $\mathrm{P}-\mathrm{by}-\mathrm{P}$ and $\mathrm{Q}-\mathrm{by}-\mathrm{Q}$ identity matrices.

统计代写|回归分析作业代写Regression Analysis代考|Summary

This chapter reviews articulations among SWMs, eigenfunctions, and spectral functions, all three of which relate to $\mathrm{SA}$. In doing so, it also links them to geostatistics. The eigenvalues of a SWM index the nature and degree of SA in the eigenvectors of a modified SWM and also appear in the complex fraction spectral density functions used to calculate lagged spatial correlations. The cells of standardized inverse spatial covariance structures, illustrated here with the popular first- and second-order ones, contain spectral density function results. These notions interlace with concepts for PCA. Although this chapter focuses on the $\mathrm{MC}$ index of $\mathrm{SA}$, similar results may be established for both the Geary ratio (GR) and the join count statistics that are applicable to nominal measurement scale data. The linear geographic landscape furnishes many relatively simple illustrations of the connections of interest here. The two-dimensional geographic landscape furnishes more relevant, albeit more complicated, contexts and highlights map pattern visualizations, one of the most important topics of this chapter.

统计代写|回归分析作业代写Regression Analysis代考|The spectral decomposition of a SWM

Consider the geographic landscape in Fig. $2.5 \mathrm{C}$. Its rook adjacency SWM C is as follows:
$$
\left[\begin{array}{llll}
0 & 1 & 1 & 0 \
1 & 0 & 0 & 1 \
1 & 0 & 0 & 1 \
0 & 1 & 1 & 0
\end{array}\right]
$$
The Perron-Frobenius theorem states that the principal eigenvalue is contained in the interval defined by the largest and smallest row sums; therefore here $\lambda_{1}=2$. For each pair of rows or columns that is identical, an eigenvalue equals zero; therefore because the first and fourth rows/columns are identical, and the second and third rows/columns are identical, two eigenvalues equal zero. Finally the trace of this matrix equals the sum of its four eigenvalues; therefore $2+0+0+\lambda=0$, and hence an eigenvalue equals $-2$.

Eq. (2.1) for this SWM is $\lambda^{2}\left(\lambda^{2}-4\right)=0$. The first $\lambda^{2}$ term is for the two roots of zero, whereas the second term factors into $(\lambda+2)(\lambda-2)$, which is for the two roots $\pm 2$. Ord (1975) also states that the eigenvalues for this particular type of geographic surface partitioning and SWM are given by $\lambda=2\left[\operatorname{COS}\left(\frac{\mathrm{h} \pi}{2+1}\right)+\operatorname{COS}\left(\frac{\mathrm{k} \pi}{2+1}\right)\right], \mathrm{h}=1,2$ and $\mathrm{k}=1,2$. This equation yields $2(0.5+0.5)=2 ; 2(0.5-0.5)=0 ; 2(-0.5+0.5)=0$; and, $2(-0.5-0.5)=-2$.

Griffith (2000, p. 98) proves that the solution to Eq. (2.2) for this particular type of geographic surface partitioning and SWM are the eigenvectors given by
$$
\frac{2}{\sqrt{(2+1)(2+1)}}\left[\operatorname{SIN}\left(\frac{h \pi}{2+1}\right) \times \operatorname{SIN}\left(\frac{k \pi}{2+1}\right)\right]
$$
This expression produces the 4-by-4 eigenvector matrix
$$
\left[\begin{array}{rrrr}
0.5 & 0.5 & 0.5 & 0.5 \
0.5 & -0.5 & 0.5 & -0.5 \
0.5 & 0.5 & -0.5 & -0.5 \
0.5 & -0.5 & -0.5 & 0.5
\end{array}\right]
$$

回归分析代写

统计代写|回归分析作业代写Regression Analysis代考|The spectral analysis of three-dimensional data

在许多情况下，三维地理参考数据的光谱分析涉及一系列地图，一个用于指定时间序列中的每个点的地图，而不是用高程补充平面表面。Griffith 和 Heurclink (2012) 将预先光谱分析概念化扩展到这种情况。现在基于光谱密度的时空(τ,这,ν)−滞后相关函数变为，对于规则方形镶嵌和车邻接定义，以及均匀间隔的时间点，
\frac{\int_{0}^{\pi} \int_{0}^{\pi} \int_{0}^{\pi} \frac{\operatorname{Cos}(\tau \theta) \operatorname{ Cos}(\eta \varphi) \operatorname{Cos}(v t)}{\left[1-\operatorname{COS}(t)\left{\rho_{s}[\operatorname{Cos}(\theta)+ \operatorname{Cos}(\varphi)]+\rho_{T}\right}\right]^{k}} d \theta d \varphi d t}{\int_{0}^{\pi} \int_{0 }^{\pi} \int_{0}^{\pi} \frac{1}{\left[1-\operatorname{COS}(t)\left{\rho_{s}[\operatorname{CoS}( \theta)+\operatorname{CoS}(\varphi)]+\rho_{T}\right}\right]^{k}} \mathrm{~d} \theta \mathrm{d} \varphi \mathrm{dt }}, \boldsymbol{\kappa}=1,2\frac{\int_{0}^{\pi} \int_{0}^{\pi} \int_{0}^{\pi} \frac{\operatorname{Cos}(\tau \theta) \operatorname{ Cos}(\eta \varphi) \operatorname{Cos}(v t)}{\left[1-\operatorname{COS}(t)\left{\rho_{s}[\operatorname{Cos}(\theta)+ \operatorname{Cos}(\varphi)]+\rho_{T}\right}\right]^{k}} d \theta d \varphi d t}{\int_{0}^{\pi} \int_{0 }^{\pi} \int_{0}^{\pi} \frac{1}{\left[1-\operatorname{COS}(t)\left{\rho_{s}[\operatorname{CoS}( \theta)+\operatorname{CoS}(\varphi)]+\rho_{T}\right}\right]^{k}} \mathrm{~d} \theta \mathrm{d} \varphi \mathrm{dt }}, \boldsymbol{\kappa}=1,2,
其中吨表示 tw 参数，ρs表示 SA 参数，并且ρr表示时间自相关参数。该规范表示一个同时的时空过程，它是相加的，其矩阵表示由下式给出C=一世吨⊗一世s−ρsC吨⊗Cs−ρ吨C吨⊗一世s,
在哪里⊗表示克罗内克乘积数学矩阵运算，Cs表示 SWM，C吨表示时间序列连接矩阵，一世吨表示吨-by-T 识别矩阵，一世s表示n−b是−n单位矩阵，和1-\operatorname{COS}(\mathrm{t})\left{\rho_{\mathrm{s}}[\operatorname{COS}(\mathrm{u})+\operatorname{COS}(\mathrm{v })]+\rho_{\mathrm{T}}\right}1-\operatorname{COS}(\mathrm{t})\left{\rho_{\mathrm{s}}[\operatorname{COS}(\mathrm{u})+\operatorname{COS}(\mathrm{v })]+\rho_{\mathrm{T}}\right}是时空连通矩阵的极限特征值C.

另一种规范是乘法的，因此描述了一个时空滞后的过程；它的矩阵表示由下式给出
C=一世吨⊗一世s−ρs一世吨⊗Cs−ρ吨C吨⊗一世s,
及其基于光谱密度的(τ,这,ν)-滞后相关性由下式给出
对于形成完整的规则方格磷−b是−问矩形区域，
Cs=C磷⊗一世问+C问⊗一世r,在哪里Cp和C问，分别是小号在米s为一个磷长度和一个问长度线性景观，和一世磷和一世问，分别是磷−b是−磷和问−b是−问身份矩阵。

统计代写|回归分析作业代写Regression Analysis代考|Summary

本章回顾了 SWM、特征函数和谱函数之间的衔接，这三者都与小号一种. 在这样做的过程中，它还将它们与地统计学联系起来。SWM 的特征值在修改后的 SWM 的特征向量中指示 SA 的性质和程度，并且还出现在用于计算滞后空间相关性的复分数谱密度函数中。标准化逆空间协方差结构的单元（此处以流行的一阶和二阶结构进行说明）包含谱密度函数结果。这些概念与 PCA 的概念交织在一起。虽然本章着重于米C指数小号一种，对于适用于标称测量尺度数据的 Geary 比率 (GR) 和连接计数统计，可以建立类似的结果。线性地理景观提供了许多相对简单的插图来说明这里感兴趣的联系。二维地理景观提供更相关但更复杂的上下文并突出显示地图图案可视化，这是本章最重要的主题之一。

统计代写|回归分析作业代写Regression Analysis代考|The spectral decomposition of a SWM

考虑图 1 中的地理景观。2.5C. 其车邻接SWM C如下：
[0110 1001 1001 0110]
Perron-Frobenius 定理指出，主特征值包含在由最大和最小行和定义的区间内；因此在这里λ1=2. 对于每对相同的行或列，特征值等于 0；因此，由于第一和第四行/列相同，并且第二和第三行/列相同，因此两个特征值为零。最后这个矩阵的迹等于它的四个特征值之和；所以2+0+0+λ=0，因此特征值等于−2.

方程。(2.1) 对于这个 SWM 是λ2(λ2−4)=0. 首先λ2项是针对零的两个根，而第二项因素(λ+2)(λ−2)，这对于两个根±2. Ord (1975) 还指出，这种特定类型的地理表面划分和 SWM 的特征值由下式给出λ=2[COS⁡(H圆周率2+1)+COS⁡(ķ圆周率2+1)],H=1,2和ķ=1,2. 这个等式产生2(0.5+0.5)=2;2(0.5−0.5)=0;2(−0.5+0.5)=0; 和，2(−0.5−0.5)=−2.

Griffith (2000, p. 98) 证明了方程的解。(2.2) 对于这种特殊类型的地理表面划分和 SWM 是由下式给出的特征向量
2(2+1)(2+1)[罪⁡(H圆周率2+1)×罪⁡(ķ圆周率2+1)]
此表达式生成 4×4 特征向量矩阵
[0.50.50.50.5 0.5−0.50.5−0.5 0.50.5−0.5−0.5 0.5−0.5−0.50.5]

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|回归分析作业代写Regression Analysis代考|Visualizing map patterns with eigenvectors

Posted on 2022年4月25日2022年4月25日 by statistics-lab

如果你也在怎样代写回归分析Regression Analysis这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的回归分析Regression Analysis及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|回归分析作业代写Regression Analysis代考|Visualizing map patterns with eigenvectors

By convention, a SWM’s rows and columns are ordered with the same sequence of areal units. The eigenvectors of a SWM are n-by-1 vectors, with each of their rows linking to the corresponding areal unit identifier (ID) for the same row in their parent SWM. This one-to-one correspondence

enables mapping the eigenvectors of a SWM. The individual eigenvector elements simply have to be joined to their corresponding polygons in a shapefile file for visualization by ArcMap, for example.

Fig. $2.4$ portrays the extreme eigenvectors for matrix $\left(I-11^{\mathrm{T}} / \mathrm{n}\right) \times$ $\mathbf{C}(\mathbf{I}-\mathbf{1 1} / \mathrm{n})$ representing the 2010 DFW metroplex census tracts. Fig. 2.4A portrays the principal eigenvector map pattern, the maximum PSA case, which depicts a hill/valley (this would change from a hill to a valley, or vice versa, by multiplying the eigenvector by $-1$ ) roughly in the center of the region, surrounded by a trough/hill, with intermediate plateaus in the western and southeastern parts of the region. This hill map pattern is one of the common global geographic trends portrayed by eigenvectors. Another typical map pattern is an east-west gradient trend, adapting to the somewhat rectangular shape of the DFW metroplex. Fig. $2.3 \mathrm{~A}$ reveals that the hill/valley subregion in Fig. 2.4A coincides with a concentration of numerous smaller census tracts located mostly in Dallas and Tarrant Counties. In contrast, Fig. 2.4B portrays a map pattern with considerable neighboring contrasts (e.g., dark red in juxtaposition with dark green), an alternating trend that exemplifies NSA. This map pattern has its intermediate values in its periphery, encircling the stark contrasts created by the alternating trend. A comparison of Fig. 2.4A and B reveals that PSA exhibits more smoothness in its map pattern, and NSA exhibits more fragmentation in its map pattern. These tendencies are less conspicuous in visualizations of the less extreme MC values.

统计代写|回归分析作业代写Regression Analysis代考|The spectral analysis of one-dimensional data

A simple one-dimensional geographic landscape (e.g., Fug. $2.5 \mathrm{~A}$ ) illustrates the connection between the spatial frequency and spatial spectral domains, furnishing the basis of the spectral density function equations presented in this section. SA indicates how rapidly a map pattern changes across a geographic landscape, using randomness as its yardstick. SA contains information about the expected frequency content mentioned earlier in this chapter. Meanwhile, the spectral density function furnishes one

mathematical link between $\mathrm{SA}$ and eigenfunctions in the spectral domain (Section 2.1; Bartlett, 1975). For a one-dimensional geographic landscape (e.g., Fig. $2.5 \mathrm{~A}$ ), given a stationary process $\left{\mathrm{X}{v}, \mathrm{t}=1,2, \ldots, \mathrm{T}\right}$ for a unidirectional dependency structure (this situation parallels a time series data structure) of the same form as the simultaneous autoregressive (SAR) model specification, $$ \mathrm{X}{\mathrm{t}}=\rho \mathrm{X}{\mathrm{t}-1}+\xi{\mathrm{t}},
$$
where $\rho$ is the autocorrelation parameter, $|\rho|<1$, t indexes location in the linear landscape, and $\xi_{t}$ is an independent and identically distributed (IID) random error term. Autocovariance functions, $\gamma(\tau), \tau=0,1, \ldots$, where $\tau$ denotes the number of lags, are established by repeatedly substituting the right-hand expression of an autoregressive equation like the preceding one into it and then applying the calculus of expectations to resulting infinite series forms of covariations. These infinite series are functions of linear combinations of $\xi_{t}^{2}$ together with powers of the SA parameter $\rho$, and hence yield $\sigma^{2}$ as well as a denominator term containing $\rho$. The corresponding atocovariance (i.e., covariation in an autocorrelated mathematical space) function is defined as follows:
$$
\gamma_{\mathrm{x}}(\tau)=\frac{\rho^{\tau} \sigma^{2}}{1-\rho^{2}}
$$
with $\tau$ being the number of lags (Griffith, 1988 , p- 111).
This preceding autocovariance function can be represented in the fretrency domain with the Fontrier transform
$$
f(\theta)=\frac{1}{2 \pi} \sum_{\tau=-\infty}^{\infty} e^{-i \pi \theta_{1}} \gamma_{X}(\tau)
$$

统计代写|回归分析作业代写Regression Analysis代考|This representation of the autocovariance

This representation of the autocovariance function in the frequency domain is referred to as the spectral density function or the spectrum of the random variable (RV) $\left{X_{t}\right}$. The sum ${ }^{6}$ of the spectrum over all frequencies gives the variance of $\left{X_{t}\right}$,
$$
\operatorname{VAR}\left(X_{t}\right)=\int_{0}^{\pi} \frac{\sigma^{2}}{2 \pi\left[1+\rho^{2}-2 \rho \operatorname{COS}(\theta)\right]} d \theta=\frac{\sigma^{2}}{2\left(1-\rho^{2}\right)},|\rho|<1,
$$
whereas the covariance at $\operatorname{lng} \tau$ is given by
$$
\operatorname{COV}\left(X_{t} X_{t-1}\right)=\int_{0}^{\pi} \frac{\sigma^{2} \operatorname{COS}(\tau \theta)}{2 \pi\left[1+\rho^{2}-2 \rho \operatorname{COS}(\theta)\right]} d \theta=\frac{\rho^{\tau} \sigma^{2}}{2\left(1-\rho^{2}\right)},|\rho|<1 .
$$
$\tau=0$ yields Eq. (2.6). In other words, representing the autocovariance function in the frequency domain allows a decomposition of the variance into frequency components that reveals their relative importance. The common effect of variance inflation routinely mentioned as a primary result of SA is apparent here: its arithmetic source is the term $-\rho^{2}$ appearing in the denominator of this expression. When no $S A$ is present, $\rho=0$ and $f(\theta)=\sigma^{2} / 2 \pi$, which is the spectral density for white noise. Accordingly, the variance in this independent observations case reduces to:

$$
\operatorname{VAR}\left(X_{\tau}\right)=\int_{0}^{\pi} \frac{\sigma^{2}}{2 \pi} \mathrm{d} \theta=\frac{\sigma^{2}}{2},
$$
which is consistent with results from the classical central limit theorem of statistics.

Furnishing asymptotic detaik for Eqs. (2.5) and (2.6), as shown by Berman and Plemmons (1994), the eigenvalues of a binary SWM for linear lattices can be defined as
$$
\lambda_{\mathrm{i}}=2 \operatorname{COS}\left(\frac{i \pi}{n+1}\right) .
$$
For the spectral density function defined by Eq. (2.5),
$$
\begin{gathered}
\lim {n \rightarrow \infty} \frac{i}{n+1}=\theta, \ \lambda{\mathrm{i}}=2 \operatorname{COS}(\theta), \text { and } \
f(\theta)=\frac{\sigma^{2}}{2 \pi\left(1+\rho^{2}-\rho \lambda\right)} .
\end{gathered}
$$
In other words, the spectral density function contains the eigenvalues of its corresponding SWM, which reveals that the autocovariance function for the RV $\left{X_{t}\right}$ is a function of the eigenvalues of the SWM.

To illustrate the relationship between the lagged spatial correlations with the second-order spatial covariance structure matrix $(\mathbf{I}-\rho \mathbf{C})^{-2}$ the SAR model specification-consider the bidirectional and one-dimensional geographic landscape with a symmetric dependency structure; that is,
$$
\mathrm{X}{\mathrm{i}}=\rho\left(\mathrm{X}{\mathrm{i}-1}+\mathrm{X}{\mathrm{i}+1}\right)+\xi{\mathrm{i}},|\rho|<\frac{1}{2}
$$
Here the autovariances at lags 0 and $\tau$ are
$$
\gamma(0)=\mathrm{E}\left(\mathrm{X}{\mathrm{i}} \mathrm{X}{\mathrm{i}}\right)=\frac{\sigma^{2}}{\left(1-4 \rho^{2}\right)^{3 / 2}}, \text { and }
$$
$\gamma(\tau)=\mathrm{E}\left(\mathrm{X}{\mathrm{i}} \mathrm{X}{\mathrm{i}-\tau}\right)$
$=\sigma^{2} \frac{\operatorname{SIN}[\tau \pi] \text { Hypergeometric PFQ }\left[\left{\frac{1}{2}, 1,2\right},{1-\tau, 1+\tau} 1-\tau, \frac{4 p}{1+2 p}\right]}{\pi \tau(1+2 p)^{2}}$ $0<\rho<1 / 2$

回归分析代写

统计代写|回归分析作业代写Regression Analysis代考|Visualizing map patterns with eigenvectors

按照惯例，SWM 的行和列按相同的面积单位顺序排列。SWM 的特征向量是 n×1 向量，它们的每一行都链接到其父 SWM 中同一行的相应区域单位标识符 (ID)。这种一一对应

能够映射 SWM 的特征向量。例如，为了通过 ArcMap 进行可视化，单个特征向量元素只需连接到 shapefile 文件中的相应多边形即可。

如图。2.4描绘矩阵的极端特征向量(一世−11吨/n)× C(一世−11/n)代表 2010 年 DFW 大都会人口普查区。图 2.4A 描绘了主要的特征向量图模式，即最大 PSA 情况，它描绘了一座山/谷（这会从一座山变为一座山谷，反之亦然，通过将特征向量乘以−1) 大致位于该地区的中心，被一个低谷/山丘包围，在该地区的西部和东南部有中间高原。这种山图模式是特征向量描绘的常见全球地理趋势之一。另一个典型的地图模式是东西向的渐变趋势，适应了 DFW 大都会的矩形形状。如图。2.3 一种揭示了图 2.4A 中的丘陵/山谷次区域与主要位于达拉斯和塔兰特县的众多较小人口普查区的集中相吻合。相比之下，图 2.4B 描绘了具有相当大的相邻对比度的地图图案（例如，深红色与深绿色并列），这是 NSA 的一种交替趋势。该地图模式在其外围具有中间值，围绕着由交替趋势产生的鲜明对比。图 2.4A 和 B 的比较表明，PSA 在其图谱中表现出更多的平滑度，而 NSA 在其图谱中表现出更多的碎片化。这些趋势在不太极端的 MC 值的可视化中不太明显。

统计代写|回归分析作业代写Regression Analysis代考|The spectral analysis of one-dimensional data

一个简单的一维地理景观（例如，Fug.2.5 一种) 说明了空间频率域和空间谱域之间的联系，为本节介绍的谱密度函数方程提供了基础。SA 表示地图模式在地理景观中的变化速度，使用随机性作为衡量标准。SA 包含有关本章前面提到的预期频率内容的信息。同时，谱密度函数提供了一个

之间的数学联系小号一种和谱域中的特征函数（第 2.1 节；Bartlett，1975）。对于一维地理景观（例如，图 1）。2.5 一种)，给定一个平稳过程\left{\mathrm{X}{v}, \mathrm{t}=1,2, \ldots, \mathrm{T}\right}\left{\mathrm{X}{v}, \mathrm{t}=1,2, \ldots, \mathrm{T}\right}对于与同步自回归 (SAR) 模型规范相同形式的单向依赖结构（这种情况与时间序列数据结构平行），X吨=ρX吨−1+X吨,
在哪里ρ是自相关参数，|ρ|<1, t 索引线性景观中的位置，以及X吨是独立同分布 (IID) 随机误差项。自协方差函数，C(τ),τ=0,1,…，在哪里τ表示滞后数，通过反复代入与前一个类似的自回归方程的右手表达式，然后将期望计算应用于所得的无限级数形式的协变来建立。这些无穷级数是线性组合的函数X吨2连同 SA 参数的幂ρ，因此产量σ2以及包含的分母项ρ. 相应的原子协方差（即自相关数学空间中的协变）函数定义如下：
CX(τ)=ρτσ21−ρ2
和τ是滞后的数量（Griffith，1988，p-111）。
前面的自协方差函数可以用 Fontrier 变换在频域中表示
F(θ)=12圆周率∑τ=−∞∞和−一世圆周率θ1CX(τ)

统计代写|回归分析作业代写Regression Analysis代考|This representation of the autocovariance

这种自协方差函数在频域中的表示称为谱密度函数或随机变量 (RV) 的谱\left{X_{t}\right}\left{X_{t}\right}. 总和6在所有频率上的频谱给出方差\left{X_{t}\right}\left{X_{t}\right},
曾是⁡(X吨)=∫0圆周率σ22圆周率[1+ρ2−2ρCOS⁡(θ)]dθ=σ22(1−ρ2),|ρ|<1,
而协方差在液化天然气⁡τ是（谁）给的
冠状病毒⁡(X吨X吨−1)=∫0圆周率σ2COS⁡(τθ)2圆周率[1+ρ2−2ρCOS⁡(θ)]dθ=ρτσ22(1−ρ2),|ρ|<1.
τ=0产生方程。(2.6)。换句话说，在频域中表示自协方差函数允许将方差分解为频率分量，从而揭示它们的相对重要性。作为 SA 的主要结果，经常提到的方差膨胀的共同影响在这里很明显：它的算术来源是术语−ρ2出现在这个表达式的分母中。没有时小号一种存在，ρ=0和F(θ)=σ2/2圆周率，这是白噪声的频谱密度。因此，这种独立观察情况下的方差减少到：曾是⁡(Xτ)=∫0圆周率σ22圆周率dθ=σ22,
这与统计的经典中心极限定理的结果一致。

为 Eqs 提供渐近细节。(2.5) 和 (2.6)，如 Berman 和 Plemmons (1994) 所示，线性格的二进制 SWM 的特征值可以定义为
λ一世=2COS⁡(一世圆周率n+1).
对于方程定义的谱密度函数。(2.5),
$$
\begin{gathered}
\lim {n \rightarrow \infty} \frac{i}{n+1}=\theta, \ \lambda {\mathrm{i}}=2 \operatorname{COS }(\theta), \text { 和 } \
f(\theta)=\frac{\sigma^{2}}{2 \pi\left(1+\rho^{2}-\rho \lambda\right )} 。
\end{gathered}
$$
换句话说，谱密度函数包含其对应 SWM 的特征值，这表明 RV 的自协方差函数\left{X_{t}\right}\left{X_{t}\right}是 SWM 特征值的函数。

为了说明滞后空间相关性与二阶空间协方差结构矩阵之间的关系(一世−ρC)−2SAR模型规范——考虑具有对称依赖结构的双向一维地理景观；那是，
X一世=ρ(X一世−1+X一世+1)+X一世,|ρ|<12
这里的自方差滞后 0 和τ是
C(0)=和(X一世X一世)=σ2(1−4ρ2)3/2, 和
C(τ)=和(X一世X一世−τ)
=\sigma^{2} \frac{\operatorname{SIN}[\tau \pi] \text { 超几何 PFQ }\left[\left{\frac{1}{2}, 1,2\right},{ 1-\tau, 1+\tau} 1-\tau, \frac{4 p}{1+2 p}\right]}{\pi \tau(1+2 p)^{2}}=\sigma^{2} \frac{\operatorname{SIN}[\tau \pi] \text { 超几何 PFQ }\left[\left{\frac{1}{2}, 1,2\right},{ 1-\tau, 1+\tau} 1-\tau, \frac{4 p}{1+2 p}\right]}{\pi \tau(1+2 p)^{2}} 0<ρ<1/2

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|回归分析作业代写Regression Analysis代考|Principal components analysis: A reconnaissance

Posted on 2022年4月25日2022年4月25日 by statistics-lab

如果你也在怎样代写回归分析Regression Analysis这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的回归分析Regression Analysis及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|回归分析作业代写Regression Analysis代考|Principal components analysis: A reconnaissance

Eigendecomposition (i.e., rewriting a matrix in terms of its eigenvalues and eigenvectors) of a correlation matrix produces a set of eigenvalues that can be arranged in descending order, along with their corresponding eigenvectors. These eigenvectors are referred to as principals components (PCs) and have the intriguing property that the amount of variance they capture follows the same order as their magnitudes. In other words, the first eigenvector sum$\mathrm{~ m a n i z e s ~ t h e ~ m u s l ~ v a n i a n e , ~ t h e ~ s e c o n d ~ c i g c u v e l t e n ~ s u m u a r e s s ~ t h e ~ s e c u a}$ largest amount of varianec, and so forth. Because the first few cigenvectors often are sufficient for representing most of the information contained in their correlation matrix, principal components analysis (PCA) commonly is used for variable selection. However, here we use PCA to illustrate linkages between eigenvectors and SA.

Griffith (1984) began to explore the application of PCA to the binary SWM C, initially making little headway because the analysis was of $n$ indicator variable correlation (i.e., phi) coefficients. Later, a simple modification of matrix $\mathbf{C}$ illuminated a breakthrough: adding an identity matrix to $\mathbf{C}$ [i.e., $(\mathbf{C}+\mathbf{I})$ ] renders a SWM mimicking a correlation matrix, allowing the application of conventional PCA to it in a way that yields interpretable results (see Appendix 2.A). Furthermore, based on the mathematical properties of eigenvalues and eigenvectors, matrices $(\mathbf{C}+\mathbf{I})$ and $\mathbf{C}$ have the same eigenvectors and the same eigenvalues if one is added to the eigenvalues of matrix $\mathrm{C}$ (i.e., $\lambda_{j}+1$ ). The resulting PCA gives an important insight into the asymptotic relationship between the $\mathrm{SWM} \mathrm{C}$ eigenvectors and $\mathrm{SA}$ : the second $\mathrm{PC}$ corresponds to the maximum positive SA (PSA), and the last $\mathrm{PC}$ to the maximum negative SA (NSA). More specifically, PCA made possible the discovery of, and now makes obvious, the fundamental theorem of MESF, which pertains to matrix $\left(\mathrm{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathbf{C}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right)$ .

统计代写|回归分析作业代写Regression Analysis代考|The spectral decomposition of a modified SWM

The MC can be written in matrix form as
The modified matrix $\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathrm{C}\left(\mathrm{I}-11^{\mathrm{T}} / \mathrm{n}\right)$ in its numerator is the matrix that relates to SA. Accordingly, the pair of eigenfunction problems becomes
$$
\operatorname{Det}\left[\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathbf{C}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right)-\lambda \mathbf{I}\right]=0
$$
and
$$
\left[\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathbf{C}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right)-\lambda_{\mathrm{j}} \mathbf{I}\right] \mathbf{E}_{\mathrm{j}}=0, \mathrm{j}=1,2, \ldots, \mathrm{n}
$$

subject to $\mathbf{E}{j}^{\mathrm{T}} \mathbf{E}{j}=1$ and $\mathbf{E}{j}^{\mathrm{T}} \mathbf{E}{\mathrm{k}}=0, j \neq k$. Because matrix $\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \times$ $\mathbf{C}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right)$ is square and symmetric, it can be decomposed into a series of rank 1 matrices consisting of the products of the eigenvalues and eigenvectors; that is,
$$
\left(\mathbf{I}-\frac{11^{\mathrm{T}}}{n}\right) \mathbf{C}\left(\mathbf{I}-\frac{11^{\mathrm{T}}}{n}\right)=\sum_{j=1}^{n} \lambda_{j} \mathbf{E}{j} \mathbf{E}{j}^{\mathrm{T}}
$$
This right-hand summation expression is a matrix expansion of the standard eigendecomposition $\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathbf{C}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right)=\mathbf{E} \Lambda \mathbf{E}^{\mathrm{T}}$, where $\Lambda$ is the diagonal matrix containing the n eigenvalues $\lambda_{\mathrm{j}}$

统计代写|回归分析作业代写Regression Analysis代考|Representing the MC with eigenfunctions

Let vector $\mathbf{Y}=\mathbf{E}{j}$. Next, substitute $\mathbf{E}{j}$ into Eq. (2.4):
$$
\begin{gathered}
{\left[\mathrm{n} /\left(\mathbf{1}^{\mathrm{T}} \mathbf{C} 1\right)\right] \mathbf{E}{\mathrm{j}}^{\mathrm{T}}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathbf{C}(\mathbf{I}-\mathbf{1 1} / \mathrm{T}) \mathbf{E}{\mathrm{j}} /} \
{\left[\mathbf{E}{\mathrm{j}}^{\mathrm{T}}\left(\mathbf{I}-\mathbf{1 1} \mathbf{T}^{\mathrm{T}} / \mathrm{n}\right) \mathbf{E}{\mathrm{j}}\right]=\left[\mathrm{n} /\left(\mathbf{1}^{\mathrm{T}} \mathbf{C} 1\right)\right] \lambda_{\mathrm{j}} / 1}
\end{gathered}
$$
which is the same as Eq. (2.3). This outcome highlights why the extreme eigenvalues of matrix $\left(\mathrm{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathbf{C}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right), \lambda_{1}$ and $\lambda_{\mathrm{m}}$, respectively, define the maximum and minimum values of a $\mathrm{MC}$ – they optimize its Rayleigh quotient. This feature of the MC distinguishes it from a Pearson product moment correlation coefficient: it does not have extreme values of $\pm 1$ but rather has an upper bound that often exceeds 1 by as much as $0.15$, or more, and a lower bound that often is closer to $-0.5$ than to $-1$.

Fig. 2.3A portrays the 2010 census tract surface partitioning $(n=1052)$ for the Dallas-Fort Worth (DFW) metroplex, and Fig. 2.3B is ArcMap SA output. The principal eigenvalue for this surface partitioning is $6.2675604$, based on the rook’s contiguity, with $1^{\mathrm{T}} \mathbf{C} 1=5626$. Therefore for PSA, $\mathrm{MC}=(1052 / 5626)(6.2675604)=1.171965$. This maximum PSA value exceeds 1 by $>0.17$. Meanwhile, for $\mathrm{NSA}, \quad \mathrm{MC}=(1052 / 5626) \times$ $(-3.949034)=-0.738426$. This maximum NSA value is closer to $-0.5$ than to $-1$.

回归分析代写

统计代写|回归分析作业代写Regression Analysis代考|Principal components analysis: A reconnaissance

相关矩阵的特征分解（即，根据其特征值和特征向量重写矩阵）产生一组可以按降序排列的特征值及其对应的特征向量。这些特征向量被称为主成分 (PC)，并且具有一个有趣的特性，即它们捕获的方差量与其大小遵循相同的顺序。换句话说，第一个特征向量和米一种n一世和和s 吨H和米在sl 在一种n一世一种n和, 吨H和 s和C这nd C一世GC在在和l吨和n s在米在一种r和ss 吨H和 s和C在一种最大量的 varianec，依此类推。由于前几个特征向量通常足以表示其相关矩阵中包含的大部分信息，因此主成分分析（PCA）通常用于变量选择。然而，这里我们使用 PCA 来说明特征向量和 SA 之间的联系。

Griffith (1984) 开始探索将 PCA 应用于二进制 SWM C，最初进展不大，因为分析是n指标变量相关（即phi）系数。后来对矩阵进行了简单的修改C阐明了一个突破：将单位矩阵添加到C[IE，(C+一世)] 呈现模拟相关矩阵的 SWM，允许以产生可解释结果的方式将常规 PCA 应用于它（参见附录 2.A）。此外，基于特征值和特征向量的数学性质，矩阵(C+一世)和C如果将一个添加到矩阵的特征值中，则具有相同的特征向量和相同的特征值C（IE，λj+1）。由此产生的 PCA 提供了一个重要的洞察力之间的渐近关系小号在米C特征向量和小号一种：第二磷C对应于最大正 SA (PSA)，最后一个磷C到最大负 SA (NSA)。更具体地说，PCA 使MESF 基本定理的发现成为可能，并且现在使之变得显而易见，该定理与矩阵有关(一世−11吨/n)C(一世−11吨/n) .

统计代写|回归分析作业代写Regression Analysis代考|The spectral decomposition of a modified SWM

MC 可以写成矩阵形式为
修改后的矩阵(一世−11吨/n)C(一世−11吨/n)在其分子中是与 SA 相关的矩阵。因此，这对特征函数问题变为
这⁡[(一世−11吨/n)C(一世−11吨/n)−λ一世]=0
和
[(一世−11吨/n)C(一世−11吨/n)−λj一世]和j=0,j=1,2,…,n

服从 \ \ mathbf {E} {j} ^ {mathrm {T}} th mathbf {E} {j}一种nd\ mathbf {E} {j} ^ {th mathrm {T}} \ mathbf {E} {th mathrm {k}} = 0, j \neq k.乙和C一种在s和米一种吨r一世X\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \times\mathbf{C}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right)一世ssq在一种r和一种nds是米米和吨r一世C,一世吨C一种nb和d和C这米p这s和d一世n吨这一种s和r一世和s这Fr一种nķ1米一种吨r一世C和sC这ns一世s吨一世nG这F吨H和pr这d在C吨s这F吨H和和一世G和n在一种l在和s一种nd和一世G和n在和C吨这rs;吨H一种吨一世s,$
\left(\mathbf{I}-\frac{11^{\mathrm{T}}}{n}\right) \mathbf{C}\left(\mathbf{I}-\frac{11^{\ mathrm{T}}}{n}\right)=\sum_{j=1}^{n} \lambda_{j} \mathbf{E} {j} \mathbf{E} {j}^{\mathrm{ T}}
$$
这个右手求和表达式是标准特征分解的矩阵展开(一世−11吨/n)C(一世−11吨/n)=和Λ和吨，在哪里Λ是包含 n 个特征值的对角矩阵λj

统计代写|回归分析作业代写Regression Analysis代考|Representing the MC with eigenfunctions

让向量是=和j. 接下来，替换和j进入方程。(2.4):
[n/(1吨C1)]和j吨(一世−11吨/n)C(一世−11/吨)和j/ [和j吨(一世−11吨吨/n)和j]=[n/(1吨C1)]λj/1
这与等式相同。(2.3)。这个结果突出了为什么矩阵的极端特征值(一世−11吨/n)C(一世−11吨/n),λ1和λ米，分别定义a的最大值和最小值米C– 他们优化了瑞利商。MC 的这一特征将其与 Pearson 乘积矩相关系数区分开来：它没有极值±1而是有一个经常超过 1 的上限0.15，或更多，以及通常更接近的下限−0.5比−1.

图 2.3A 描绘了 2010 年人口普查区域的表面划分(n=1052)对于达拉斯-沃思堡 (DFW) 大都市，图 2.3B 是 ArcMap SA 输出。这种表面划分的主要特征值为6.2675604，基于车的邻接性，与1吨C1=5626. 因此对于 PSA，米C=(1052/5626)(6.2675604)=1.171965. 此最大 PSA 值超过 1>0.17. 同时，对于ñ小号一种,米C=(1052/5626)× (−3.949034)=−0.738426. 这个最大的 NSA 值更接近−0.5比−1.

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|回归分析作业代写Regression Analysis代考|An introduction to spectral

Posted on 2022年4月25日2022年4月25日 by statistics-lab

如果你也在怎样代写回归分析Regression Analysis这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的回归分析Regression Analysis及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|回归分析作业代写Regression Analysis代考|An introduction to spectral

统计代写|回归分析作业代写Regression Analysis代考|Representing SA in the spectral domain

A close relationship exists between SA and the spectral domain (see Bartlett, 1975). A spatial domain refers to how a map pattern changes over space, with this geographic variation relating to SA, whereas a spectral domain refers to how much of the map pattern lies within each given frequency band over a range of frequencies, which constitutes a spectrum. A mathematical function relates these two domains.

Tiefelsdorf and Boots $(1995)$ establish an important link between a n-by-n SWM C and SA: the eigenvalues of a modified SWM, namely, the Moran coefficient $(\mathrm{MC})$ numerator matrix expression $\left(\mathrm{I}-11^{\mathrm{T}} / \mathrm{n}\right) \times$ $\mathbf{C}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right)$ involving pre- and postmultiplication of a $\mathrm{SWM}$ by a standard projection matrix, ${ }^{3}$ index all possible distinct natures and degrees of $\mathrm{SA}$ associated with a given SWM. This set of eigenvalues constitutes a spectrum. Griffith (1996) establishes the accompanying link between SA and map pattern: a linear combination of the eigenvectors of the aforementioned modified SWM describes the map pattern exhibited by a geographic distribution.

统计代写|回归分析作业代写Regression Analysis代考|From a spatial frequency to a spatial spectral domain

Table $2.1$ and Fig. $2.1$ present a common interface between spatial analysts and spectral concepts, namely, a remotely sensed satellite image. Here a multisensor instrument records wavelength measurements of electromagnetic radiation, with each discrete, distinctly recorded wavelength interval measured by a sensor constituting a band. In this context, the term spectrum refers to classifying a measurement according to its position on a scale between two extreme or opposite points. This general definition acknowledges that many types of measurements can be labeled spectra. Those of interest in this chapter include SWM eigenvalues and spatial correlations. A glass prism 4 exemplifies the notion of a spectrum specifically with regard to remotely sensed images (Fig. $2.2 \mathrm{~A}$ ).

The notion of a spectrum implies two distinct reference points for spatial statistical analysis. One is known as the frequency domain, and the other is known as the spectral domain. A spatial frequency domain refers to the frequency with which map attribute values change over a geographic landscape. This is the domain in which MESF operates. It relates to spatial autoregression and hence to inverse spatial covariance matrices constructed with SWMs. The other – the spectral domain – deals with spatial correlation and furnishes selected geographic landscape equations (i.e., spectral density functions) for calculating these correlations. This is the domain in which geostatistics operates. It relates to semivariogram models and hence to spatial covariance matrices (rather than their inverses). SWMs, among other mathematical tools, bridge these two domains (with the matrix inversion operation difference between them magnifying geographic edge effects between these two forms of spatial statistical analysis). This chapter highlights MESF eigenvalues that appear in spectral density functions, emphasizing this linkage.

统计代写|回归分析作业代写Regression Analysis代考|Eigenvalues and eigenvectors

Multivariate statistical analysis is perhaps the most common subject area in which researchers and students alike first encounter eigenfunctions. In this setting, calculations of these mathematical quantities are for correlation and covariance matrices, among others, and they relate to patterns of multicollinearity. Consequently, that eigenfunctions for SWMs are useful and illuminating should not be a surprise.

Regardless of whether a correlation matrix, a SWM, or some other square matrix is of interest, calculation of eigenfunctions remains the same. Eigenvalues for a given real $n$-by-n matrix $C$ are the $n$ roots of the polynomial defined by.
$$
\operatorname{Det}(\mathbf{C}-\lambda \mathbf{I})=0,
$$
where Det denotes the matrix determinant operation, and $\lambda$ denotes an eigenvalue. The solution to this $n$ th-order polynomial is the set of $n$ eigenvalues $\lambda_{y}, j=1,2, \ldots, n$. If a real matrix is symmetric, then its eigenfunctions are guaranteed to be real numbers, and its eigenvectors are mutually orthogonal. Pairing with each eigenvalue is an $\mathrm{n}$-by-1 eigenvector satisfying the following equation:
$$
\left(\mathbf{C}-\lambda_{j} \mathbf{I}\right) \mathbf{E}_{j}=\mathbf{0}, \mathbf{j}=1,2, \ldots, \mathrm{n}
$$

where $\mathbf{E}{j}$ denotes the jth eigenvector, and $\mathbf{E}{j} \neq 0$ (the trivial solution), with Eq. (2.2) being constrained such that
$$
\mathbf{E}{j}{ }^{\mathrm{T}} \mathbf{E}{j}=1 \text { (normalization), and } \mathbf{E}{j}{ }^{\mathrm{T}} \mathbf{E}{\mathrm{k}}=0 \text { (orthogonality) } \mathrm{j} \neq \mathrm{k} \text {. }
$$
Because normalization is a sum-of-squares restriction, it reveals that the eigenvectors are unique except for a multiplicative factor of $-1$. Although these eigenvectors are orthogonal, they are not uncorrelated. The PerronFrobenius theorem ensures that the principal eigenvector of SWM $C$ has all nonnegative elements. Notably, the matrix $\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right)$ in the modified matrix expression $\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathrm{C}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right)$ replaces the principal eigenvector of matrix $\mathbf{C}$ with one proportional to vector 1 and centers (i.e., forces a mean of zero for) the remaining $\mathrm{n}-1$ eigenvectors, resulting in them being mutually uncorrelated as well as mutually orthogonal.

The uumume of Eys. $(2.1)$ and (2.2) is the folluwiug sel ol a MC values that index the nature and degree of $\mathrm{SA}$ in their corresponding eigenvectors:
$$
\begin{aligned}
\mathrm{MC}{\mathrm{j}} &=\frac{\mathrm{n} \quad \mathbf{E}{\mathrm{j}}^{\mathrm{T}}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathbf{C}(\mathbf{I}-\mathbf{1 1} / \mathrm{n}) \mathbf{E}{\mathrm{j}}^{\mathrm{T}}}{1^{\mathrm{T}} \mathrm{C} 1}=\frac{\mathrm{n}}{\mathbf{E}^{\mathrm{T}}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathbf{E}{\mathrm{j}}}=\frac{\mathbf{E}{\mathrm{j}}^{\mathrm{T}} \mathbf{C E}{j}}{\mathbf{E}{j}^{\mathrm{T}} \mathbf{E}{\mathrm{j}}}=\frac{\mathrm{n}}{1^{\mathrm{T}} \mathbf{C 1}} \frac{\lambda_{\mathrm{j}}}{1} \
&=\lambda_{\mathrm{j}} \frac{\mathrm{n}}{1^{\mathrm{T}} \mathrm{C1}} ;
\end{aligned}
$$
and a set of $n$ eigenvectors that portrays the full range of SA, from maximum positive to maximum negative, for a posited SWM characterizing a given geographic landscape surface partitioning.

回归分析代写

统计代写|回归分析作业代写Regression Analysis代考|Summary

本章介绍了支持在地理参考数据分析中识别并有效和有效地解释和处理 SA 问题的动机论点的发现。它的讨论始于对各种微妙不同的定义观点的处理小号一种，在地图图案方面强调这个概念。托布勒第一地理定律的数学公式化遵循定义 SA。量化 SA 的一个关键要素是 SWM 的规范，其两种最流行的形式用矩阵表示C，定义为n基于一组区域单元的拓扑结构和矩阵的二进制零一指标在，矩阵 C 的行标准化版本。 SWM 能够定位不同的指数来量化特定于不同数据测量尺度类型的 SA。在这些指数中，最受欢迎的是米C，它是为区间/比率数据测量尺度而开发的，但已扩展到名义和有序数据测量尺度。因此，本章介绍了米C抽样分布理论，这对于统计推断目的至关重要。下一节（第 1.2 节）讨论 SA 对统计分析的影响，强调它影响方差的各种方式。然后讨论将 SA 情境化为违反经典统计的 IID 假设，以及如何使用地图和 Moran 散点图以及其他图形工具对其进行可视化。尽管 SA 文献侧重于其对方差的影响，但最后的实质性/教学背景部分提供的插图显示了 SA 如何更普遍地修改直方图的形状。

统计代写|回归分析作业代写Regression Analysis代考|The mean and variance of the MC for linear

继 Clift 和 Ord (1973) 之后，Upton 和 Fingleton (1985, p. 338) 表明米C对于线性回归残差，对于空间
自相关 23
小号在米C是对称的，协变量的数量是磷, 如下, 其中米=一世−X(X吨X)−1X吨是线性回归理论的标准投影矩阵：
\begin{聚集} E(M C)=\frac{n}{\mathbf{1}^{T} \mathbf{C 1}} \frac{\operatorname{TR}\left{\left[\mathbf{I }-\mathbf{X}\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right)^{-1} \mathbf{X}^{\mathrm{T}}\右] \mathbf{C}\right}}{\mathrm{n}-\mathrm{k}}, \text { 和 } \ \operatorname{VAR}(\mathrm{MC})=2\left(\frac {\mathrm{n}}{\mathbf{1}^{\mathbf{T}} \mathbf{C} 1}\right)^{2}\left[\frac{\operatorname{TR}\left{\左[\mathbf{I}-\mathbf{X}\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right)^{-1} \mathbf{X}^{\ mathrm{T}}\right] \mathbf{C}\left[\mathbf{I}-\mathbf{X}\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right )^{-1} \mathbf{X}^{\mathrm{T}}\right] \mathbf{C}\right}}{(\mathrm{n}-\mathrm{k})(\mathrm{n }-\mathrm{k}+2)}\对。\ \left.-\frac{\left.\begin{gathered} E(M C)=\frac{n}{\mathbf{1}^{T} \mathbf{C 1}} \frac{\operatorname{TR}\left{\left[\mathbf{I}-\mathbf{X}\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right)^{-1} \mathbf{X}^{\mathrm{T}}\right] \mathbf{C}\right}}{\mathrm{n}-\mathrm{k}}, \text { and } \ \operatorname{VAR}(\mathrm{MC})=2\left(\frac{\mathrm{n}}{\mathbf{1}^{\mathrm{T}} \mathbf{C} 1}\right)^{2}\left[\frac{\operatorname{TR}\left{\left[\mathbf{I}-\mathbf{X}\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right)^{-1} \mathbf{X}^{\mathrm{T}}\right] \mathbf{C}\left[\mathbf{I}-\mathbf{X}\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right)^{-1} \mathbf{X}^{\mathrm{T}}\right] \mathbf{C}\right}}{(\mathrm{n}-\mathrm{k})(\mathrm{n}-\mathrm{k}+2)}\right. \ \left.-\frac{\left.\left(\operatorname{TR}\left{\left[\mathbf{I}-\mathbf{X}\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right)^{-1} \mathbf{X}^{\mathrm{T}}\right] \mathbf{C}\right}\right)^{2}\right]}{(\mathrm{n}-\mathrm{k})^{2}}\right] \end{gathered}
在哪里ķ=p+1.
对于以下情况，假设Xj与矩阵的主特征向量成正比(一世−11吨/n)C(一世−11/吨)，其特征值为λ1，这导致最大程度的 PSA（更坏的情况）。平面分割的最大主特征值是这样的λ1≤一种+2n−b, 对于适当计算的实数 a 和b（Griffith \& Sone，1995 年，第 170 页）。然而，大多数经验表面分区更多地涉及规则正方形和规则六边形镶嵌的混合。此外，大多数经验曲面没有任何面积单位，其邻域数是 n 的函数。相反，具有 30 个或更多 rook 邻接定义的邻居的区域单元很少见。因此，它们的主要特征值更接近 6，而不是n.

统计代写|回归分析作业代写Regression Analysis代考|Some multicollinearity among the covariates

随着协变量数量的增加，此处呈现的渐近方差的收敛趋于变慢。尽管如此，这是一个很好的

近似的情况下n−ķ具有实际量级（例如，至少 100).

表 1.A.1 总结了一个数值示例的结果，其中面积单位的数量和地理配置各不相同。案例 II 指出的一个修改是，相关的多个协变量被它们的主成分替换，以一种降维的方式，这降低了ķ在分母中（可以提出不减少的论点ķ）。此外，受约束的最大六边形镶嵌具有标记为 1 和n环绕一个完整矩形区域的外部，但受到限制，因此它们的最大邻居数为 30 。该表中的结果证实了以下论点：米C因为回归残差是一个很好的近似值，只要矩阵的主特征值C不是的函数n, 没有面积单位的邻居数是n，并且协变量的数量不是n. Griffith (2010) 在没有协变量的情况下证明了同样的结果。这里的一个重要指标是n−ķ，它需要相对较大才能使渐近标准误差成为良好的近似值。表 1.A.1 中该表达式的最小值是 97 ，其近似值非常好。结果n<50在线性回归环境中往往很差，而结果n<25在单变量环境中往往很差（即没有协变量）。

的期望值米C比标准误更容易计算；这个数量变为零，因为n走向无穷大。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|回归分析作业代写Regression Analysis代考|Summary

Posted on 2022年4月25日2022年4月25日 by statistics-lab

如果你也在怎样代写回归分析Regression Analysis这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的回归分析Regression Analysis及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|回归分析作业代写Regression Analysis代考|Summary

This chapter presents findings supporting the motivating contention that recognizing and efficiently and effectively accounting for and handling SA matters in georeferenced data analyses. Its discussion begins with a treatment of various subtly different definitional perspectives about $\mathrm{SA}$, emphasizing this concept in terms of map pattern. A mathematical formularization of Tobler’s First Law of Geography follows defining SA. A critical element of quantifying SA is specification of a SWM, whose two most popular forms are denoted by matrix $\mathbf{C}$, defined in terms of $\mathrm{n}$ binary zero-one indicators based upon the topological structure of a set of areal units, and matrix $\mathbf{W}$, the row-standardized version of matrix C. A SWM enables the positing of different indices to quantify SA that are specific to different data measurement scale types. Of these indices, the most popular is the $\mathrm{MC}$, which was developed for interval/ratio data measurement scales but has been extended to nominal and ordinal data measurement scales. Accordingly, this chapter presents the basics of the $\mathrm{MC}$ sampling distribution theory, which is essential for statistical inference purposes. The next section (Section 1.2) addresses impacts of SA on statistical analyses, stressing various ways it affects variance. Then discussion turns to SA contextualized as a violation of the IID assumption of classical statistics, and how it can be visualized with maps and with a Moran scatterplot, as well as with other graphical tools. Although the SA literature focuses on its impact upon variance, the last substantive/pedagogic background section furnishes illustrations showing how SA more generally can modify the shape of histograms.

统计代写|回归分析作业代写Regression Analysis代考|The mean and variance of the MC for linear

Following Clift and Ord (1973), Upton and Fingleton (1985, p. 338) show that the mean and variance of the $\mathrm{MC}$ for linear regression residuals, for
Spatial autocorrelation 23
which the $S W M C$ is symmetric and the number of covariates is $\mathrm{P}$, are as follows, where $\mathbf{M}=\mathbf{I}-\mathbf{X}\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right)^{-1} \mathbf{X}^{\mathrm{T}}$ is the standard projection matrix from linear regression theory:
$$
\begin{gathered}
E(M C)=\frac{n}{\mathbf{1}^{T} \mathbf{C 1}} \frac{\operatorname{TR}\left{\left[\mathbf{I}-\mathbf{X}\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right)^{-1} \mathbf{X}^{\mathrm{T}}\right] \mathbf{C}\right}}{\mathrm{n}-\mathrm{k}}, \text { and } \
\operatorname{VAR}(\mathrm{MC})=2\left(\frac{\mathrm{n}}{\mathbf{1}^{\mathrm{T}} \mathbf{C} 1}\right)^{2}\left[\frac{\operatorname{TR}\left{\left[\mathbf{I}-\mathbf{X}\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right)^{-1} \mathbf{X}^{\mathrm{T}}\right] \mathbf{C}\left[\mathbf{I}-\mathbf{X}\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right)^{-1} \mathbf{X}^{\mathrm{T}}\right] \mathbf{C}\right}}{(\mathrm{n}-\mathrm{k})(\mathrm{n}-\mathrm{k}+2)}\right. \
\left.-\frac{\left.\left(\operatorname{TR}\left{\left[\mathbf{I}-\mathbf{X}\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right)^{-1} \mathbf{X}^{\mathrm{T}}\right] \mathbf{C}\right}\right)^{2}\right]}{(\mathrm{n}-\mathrm{k})^{2}}\right]
\end{gathered}
$$
where $\mathrm{k}=\mathrm{p}+1$.
For the following cases, suppose $\mathbf{X}{j}$ is proportional to the principal eigenvector of matrix $\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathrm{C}(\mathbf{I}-\mathbf{1 1} / \mathrm{T})$, whose eigenvalue is $\lambda{1}$, which results in the maximum degree of PSA (a worse-case scenario). The maximum principal eigenvalue for a planar surface partitioning is such that $\lambda_{1} \leq \mathrm{a}+\sqrt{2 \mathrm{n}-\mathrm{b}}$, for appropriately calculated real numbers a and $\mathrm{b}$ (Griffith \& Sone, 1995 , p. 170). However, most empirical surface partitionings relate more to a mixture of a regular square and a regular hexagonal tessellation. In addition, most empirical surfaces do not have any areal units whose number of neighbors is a function of n; rather, areal units with rook adjacency-defined neighbors of 30 or more are rare. Accordingly, their principal eigenvalues are much closer to 6 and not a function of $\mathrm{n}$.

统计代写|回归分析作业代写Regression Analysis代考|Some multicollinearity among the covariates

Convergence on the asymptotic variance presented here tends to be slower as the number of covariates increases. Nevertheless, it is a good

approximation for cases where $n-k$ is of a practical magnitude (e.g., at least 100$)$.

Table 1.A.1 summarizes results for a numerical example in which the number of areal units and the geographic configuration vary. One modification indicated by Case II is that multiple covariates that are correlated are replaced by their principal components, in a dimension-reducing way, which decreases the value of $k$ here in the denominator (an argument could be made not to decrease $k$ ). Furthermore, the constrained maximum hexagonal tessellation has areal units labeled 1 and $\mathrm{n}$ that wrap around the outside of a complete rectangular region, but constrained so that their maximum numbers of neighbors are 30 . Results in this table corroborate the contention that the asymptotic standard error of the $\mathrm{MC}$ for regression residuals is a very good approximation as long as the principal eigenvalue of matrix $C$ is not a function of $n$, no areal units have numbers of neighbors that are a function of $n$, and the number of covariates is not a function of $n$. Griffith (2010) demonstrates this same result for the case of no covariates. One important index here is $n-k$, which needs to be relatively large for the asymptotic standard error to be a good approximation. The smallest value in Table 1.A.1 for this expression is 97 , for which the approximation is quite good. Results for $\mathrm{n}<50$ tend to be poor in the linear regression context, whereas results for $\mathrm{n}<25$ tend to be poor in the univariate context (i.e., no covariates).

The expected value of the $\mathrm{MC}$ is easier to calculate than its standard error; this quantity goes to zero as $\mathrm{n}$ goes to infinity.

回归分析代写

统计代写|回归分析作业代写Regression Analysis代考|Summary

统计代写|回归分析作业代写Regression Analysis代考|The mean and variance of the MC for linear

统计代写|回归分析作业代写Regression Analysis代考|Some multicollinearity among the covariates

随着协变量数量的增加，此处呈现的渐近方差的收敛趋于变慢。尽管如此，这是一个很好的

近似的情况下n−ķ具有实际量级（例如，至少 100).

的期望值米C比标准误更容易计算；这个数量变为零，因为n走向无穷大。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|回归分析作业代写Regression Analysis代考|Different measurements for different data types

Posted on 2022年4月25日2022年4月25日 by statistics-lab

如果你也在怎样代写回归分析Regression Analysis这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的回归分析Regression Analysis及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|回归分析作业代写Regression Analysis代考|Different measurements for different data types

统计代写|回归分析作业代写Regression Analysis代考|Quantifying SA

Similar to correlation coefficients in classical statistics, a SA index may be specific to an attribute’s measurement scale (i.e., nominal, ordinal, interval, and ratio). Similar to the Pearson product moment correlation coefficient, $r$, the Moran coefficient $(\mathrm{MC})$, the most widely employed $S \mathrm{~A}$ index, can be used with all measurement scales (Griftith, 2010). The $\mathrm{MC}$, originally designed for interval/ratio data, may be defined as follows:
$\sum_{j=1}^{n} \sum_{j=1}^{n} c_{i j}\left(y_{i}-\bar{y}\right)\left(y_{j}-\bar{y}\right)$
$\frac{\sum_{i=1}^{n} \sum_{j=1}^{n} c_{i j}}{\sum_{j=1}^{n}\left(y_{i}-\bar{y}\right)^{2} / n}=\frac{n}{\sum_{i=1}^{n} \sum_{j=1}^{n} c_{i j}} \frac{\sum_{i=1}^{n}\left(y_{i}-\bar{y}\right)\left[\sum_{j=1}^{n} c_{i j}\left(y_{j}-\bar{y}\right)\right]}{(n-1) s^{2}}$

where $c_{\mathrm{ij}}$ is an entry in the SWM $\mathrm{C}, \bar{\gamma}$ is the arithmetic mean and $s^{2}$ is the sample variance of response variable $Y$, and $z_{i}$ is the $z$-score for attribute value $y_{i}$ – The numerator of the $M C$ contains the pairs of values $z_{i}$ and $\sum_{j=1}^{n} c_{i j} z_{j}$, whose graphic portrayal is the Moran scatterplot (see Section 1.2.2). Like r, the $\mathrm{MC}$ is a covariation-based index. Unlike $\mathrm{r}-$ whose extremes are $-1$ (a perfect indirect relationship) and one (a perfect direct relationship), and for which zero denotes no correlation-the MC’s extreme values essentially are a function of the smallest and second largest eigenvalues (a topic treated in ensuing sections) of the employed SWM, and for which $-1 /(n-1)$ denotes no SA for a single RV. Frequently, the smallest possible $\mathrm{MC}$ is closer to $-0.5$, whereas the largest possible $\mathrm{MC}$ is closer to 1.15. For example, the extreme MCs for the 254-county Texas $\mathrm{~ ร ु W M ~ 1 m a n 1 ~ ” I n ~ a ~ a m и}$ and based upon a paired comparisons perspective are $-0.43024$ and $0.89546$ (see de Jong, Sprenger, \& van Veen, 1984).

The Geary ratio (GR) is a second popular $\mathrm{SA}$ index formulated for interval/ratio data. Rather than being based upon cross-products (i.e., covariation), its basis is paired comparisons, or squared differences between those pairs of attribute values whose corresponding row and column entries in the SWM are a positive value. The GR may be defined as follows:
$$
\frac{\sum_{i=1}^{n} \sum_{j=1}^{n} r_{i i}\left(y_{i}-y_{j}\right)^{2} / \sum_{i=1}^{n} \sum_{j=1}^{n} r_{i i}}{2 \sum_{i=1}^{n}\left(y_{i}-\bar{y}\right)^{2} /(n-1)}=\frac{n-1}{\sum_{i=1}^{n} \sum_{j=1}^{n} c_{i j}} \frac{\sum_{i=1}^{n}\left(\sum_{j=1}^{n} r_{i i}\right)\left(y_{i}-\bar{y}\right)^{2}}{\sum_{i=1}^{n}\left(y_{i}-\bar{y}\right)^{2}}
$$

统计代写|回归分析作业代写Regression Analysis代考|Distributional theory

Distributional theory refers to the sampling distribution of a statistic, which a researcher needs for hypothesis-testing purposes. Here the common null hypothesis is zero SA. Cliff and Ord (1981) present this distributional theory for both randomly sampling an attribute from a normal RV (i.e., the normality assumption) and randomization of a given set of attribute values. They extend this former case to linear regression error terms estimated with ordinary least squares (OLS).

For the case of a single RV, the expected value of the sampling distribution of the MC for either the random sampling or randomization inferential basis is $-1 /(n-1)$, signifying zero $\mathrm{SA}$. The asymptotic standard error for this case is $\sqrt{\sum_{i=1}^{n} \sum_{j=1}^{n} c_{y}}$; this asymptotic result is extremely good by $\mathrm{n}>25$ when no covariates are included in an analysis. As $n$ goes to infinity, the sampling distribution of $\mathrm{MC}$ converges on a normal distribution. Accordingly, the test statistic is given by
$$
z=\sqrt{\sum_{i=1}^{\infty} \sum_{j=1}^{n} c_{i j}} \frac{M C+{ }_{11=1}^{1}}{\sqrt{2}} .
$$
Although the most natural alternate hypothesis is that SA is not equal to zero (i.e., a two-tailed test), because almost all geographic phenomena exhibit PSA, spatial researchers almost always could argue for an alternate hypothesis of PSA.
For linear regression residuals, the variance approximation remains useful when the number of covariates is not a function of $n$ and the spatial structure is far from a geographic maximum connectivity case (these two characteristics generally hold in practice; see Appendix 1.A). Similarly, although the expected value is a function of the covariates included in a linear regression equation specification, it tends to converge to zero from a negative value as $n$ increases, given that the number of covariates remains the same.

统计代写|回归分析作业代写Regression Analysis代考|Impacts of SA on attribute statistical distributions

The principal impact of SA is on the variance of a RV: PSA inflates variance. Table $1.1$ summarizes results from a simulation experiment in which the spatially autocorrelated RVs contain moderate PSA (approximately, MC $=0.7$ and $G R=0.3$ ). The four RVs represent the ones most commonly employed in spatial analyses. The mean does not change, whereas the variance substantially increases (c.g., a variance inflation factor of $1.2^{2}$ to $3.0^{2}$ ) once SA is embedded in a RV. Skewness (i.e., symmetry) tends to be impacted less than variance, with the Poisson RV indicating that existing skewness can be exacerbated by the presence of PSA. Finally, kurtosis (peakedness) tends to be noticeably impacted by the presence of PSA. These summary statistics reveal that the general effect of PSA is to shrink the frequencies of the more central values of a RV and to inflate the frequencies of the values located away from that RV distribution’s center (e.g., arithmetic mean): a more platykurtic distribution with fatter tails.

SA is a two-dimensional concept. As such, visualizing it helps to understand it. The nelevant systenatic urganization of geureferenced atwibute values is a map pattern. A variety of tools exist that highlight map patterns associated with SA. An obvious one is a map. Fig. $1.1$ presents five map patterns depicting different natures and degrees of SA. With regard to the preceding discussion of variance inflation, Fig. 1.1A implies that marked PSA decreases within regions variation as well as increases between regions variation. Fig. 1.1E implies that marked NSA increases within regions variation as well as decreases between regions variation.

Fig. $1.2$ presents an example of the variance inflation introduced into a normal RV by PSA. Fig. 1.2A is the histogram for independent and identically distributed (IID) random observations. Its range is roughly $-3$ to 3 . Fig. 1.2B is the histogram for these same data after embedding PSA in them. Its range is roughly $-5$ to 5 . The highest bar in Fig. $1.2 \mathrm{~A}$ is about $35 \%$, whereas the highest bar in Fig. $1.2 \mathrm{~B}$ is about $23 \%$. The tails in Fig. 1.2B are much heavier than those in Fig. 1.2A. Nevertheless, both frequency distributions center on zero, and both are reasonably symmetric.

回归分析代写

统计代写|回归分析作业代写Regression Analysis代考|Quantifying SA

与经典统计中的相关系数类似，SA 指数可能特定于属性的测量尺度（即名义、序数、区间和比率）。类似于 Pearson 积矩相关系数，r, 莫兰系数(米C), 使用最广泛的小号一种指数，可用于所有测量尺度（Griftith，2010）。这米C，最初是为区间/比率数据设计的，可以定义如下：
∑j=1n∑j=1nC一世j(是一世−是¯)(是j−是¯)
∑一世=1n∑j=1nC一世j∑j=1n(是一世−是¯)2/n=n∑一世=1n∑j=1nC一世j∑一世=1n(是一世−是¯)[∑j=1nC一世j(是j−是¯)](n−1)s2

在哪里C一世j是 SWM 中的一个条目C,C¯是算术平均值和s2是响应变量的样本方差是，和和一世是个和- 属性值得分是一世– 的分子米C包含值对和一世和∑j=1nC一世j和j，其图形描绘是 Moran 散点图（参见第 1.2.2 节）。与 r 一样，米C是一个基于协变的索引。不像r−谁的极端是−1（一个完美的间接关系）和一个（一个完美的直接关系），其中零表示没有相关性 – MC 的极值本质上是所用 SWM 的最小和第二大特征值（在随后的部分中讨论的主题）的函数, 并且为此−1/(n−1)表示单个 RV 没有 SA。通常，最小的可能米C更接近−0.5，而最大可能米C接近 1.15。例如，德克萨斯州 254 个县的极端 MCรुи Rु在米 1米一种n1 ”一世n 一种一种米一世并基于配对比较的观点是−0.43024和0.89546（见德容、斯普林格、\&范维恩，1984）。

Geary比率（GR）是第二个流行的小号一种为区间/比率数据制定的指数。其基础不是基于叉积（即协变），而是基于成对比较，或在 SWM 中对应的行和列条目为正值的那些属性值对之间的平方差。GR 可以定义如下：
∑一世=1n∑j=1nr一世一世(是一世−是j)2/∑一世=1n∑j=1nr一世一世2∑一世=1n(是一世−是¯)2/(n−1)=n−1∑一世=1n∑j=1nC一世j∑一世=1n(∑j=1nr一世一世)(是一世−是¯)2∑一世=1n(是一世−是¯)2

统计代写|回归分析作业代写Regression Analysis代考|Distributional theory

分布理论是指研究人员出于假设检验目的而需要的统计数据的抽样分布。这里常见的零假设是零 SA。Cliff 和 Ord (1981) 提出了这种分布理论，用于从正态 RV（即正态性假设）随机抽样属性和给定一组属性值的随机化。他们将前一种情况扩展到使用普通最小二乘法 (OLS) 估计的线性回归误差项。

对于单个 RV，对于随机抽样或随机化推理基础，MC 抽样分布的期望值为−1/(n−1), 表示零小号一种. 这种情况的渐近标准误是∑一世=1n∑j=1nC是; 这个渐近结果非常好n>25当分析中不包含协变量时。作为n趋于无穷大，抽样分布为米C收敛于正态分布。因此，检验统计量由下式给出
和=∑一世=1∞∑j=1nC一世j米C+11=112.
尽管最自然的替代假设是 SA 不等于 0（即双尾检验），因为几乎所有的地理现象都表现出 PSA，空间研究人员几乎总是可以支持 PSA 的替代假设。
对于线性回归残差，当协变量的数量不是n并且空间结构远不是地理最大连通性的情况（这两个特征在实践中普遍存在；见附录 1.A）。类似地，尽管期望值是线性回归方程规范中包含的协变量的函数，但它倾向于从负值收敛到零，因为n增加，因为协变量的数量保持不变。

统计代写|回归分析作业代写Regression Analysis代考|Impacts of SA on attribute statistical distributions

SA 的主要影响是对 RV 的方差：PSA 夸大了方差。桌子1.1总结了模拟实验的结果，其中空间自相关的 RV 包含中等 PSA（大约 MC=0.7和GR=0.3）。这四个 RV 代表了空间分析中最常用的那些。均值不变，而方差显着增加（cg，方差膨胀因子为1.22到3.02) 一旦 SA 嵌入到 RV 中。偏度（即对称性）受到的影响往往小于方差，泊松 RV 表明存在 PSA 会加剧现有的偏度。最后，峰度（峰度）往往会受到 PSA 的显着影响。这些汇总统计数据表明，PSA 的一般效果是缩小 RV 更中心值的频率，并夸大远离该 RV 分布中心的值的频率（例如，算术平均值）：更扁平的分布与更肥的尾巴。

SA 是一个二维的概念。因此，将其可视化有助于理解它。geureferenced atwibute 值的相关系统化是一种映射模式。存在多种突出与 SA 相关的地图模式的工具。一个明显的就是地图。如图。1.1呈现了五种地图模式，描绘了 SA 的不同性质和程度。关于前面对方差膨胀的讨论，图 1.1A 表明显着的 PSA 在区域变化内降低，而在区域变化之间增加。图 1.1E 意味着显着的 NSA 在区域变化内增加，在区域变化之间减少。

如图。1.2展示了一个由 PSA 引入正常 RV 的方差膨胀的示例。图 1.2A 是独立同分布 (IID) 随机观测的直方图。它的范围大致是−3到 3 。图 1.2B 是这些相同数据在嵌入 PSA 后的直方图。它的范围大致是−5到 5 。图中最高的柱子。1.2 一种是关于35%，而图中最高的条。1.2 乙是关于23%. 图 1.2B 中的尾部比图 1.2A 中的重得多。然而，两个频率分布都以零为中心，并且都是合理对称的。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

随机过程代考

贝叶斯方法代考

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

机器学习代写

多元统计分析代考

基础数据: $N$ 个样本， $P$ 个变量数的单样本，组成的横列的数据表
变量定性: 分类和顺序；变量定量：数值
数学公式的角度分为: 因变量与自变量

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|回归分析作业代写Regression Analysis代考|Spatial autocorrelation

Posted on 2022年4月25日2022年4月25日 by statistics-lab

如果你也在怎样代写回归分析Regression Analysis这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的回归分析Regression Analysis及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

Modeling spatial relationships—ArcGIS Pro | Documentation — 统计代写|回归分析作业代写Regression Analysis代考|Spatial autocorrelation

统计代写|回归分析作业代写Regression Analysis代考|Defining SA

The presence of nonzero correlation results in one $\mathrm{RV}$, $\mathrm{Y}$, in a pair being dependent on the other $\mathrm{RV}$, X. Its global trend depicting a positive relationship is for larger values of $X$ and $Y$ to tend to coincide, for intermediate values of $X$ and $Y$ to tend to coincide, and for smaller values of $X$ and $Y$ to tend to coincide; values of $\mathrm{X}$ are directly proportional to their corresponding values of $Y$. For an indirect (i.e., negative or inverse) relationship, larger values of $X$ tend to coincide with smaller values of $Y$, intermediate values of $X$ and $Y$ tend to coincide, and smaller values of $X$ tend to coincide with larger values of $Y$; values of $X$ are inversely proportional to their corresponding values of $Y$. A random relationship has values of $X$ and $Y$ haphazardly coinciding according to their relative magnitudes.

Autocorrelation transfers this notion of relationships from two RVs to a single RV; the prefix auto means self. Accordingly, $n$ observations have $\mathrm{n}(\mathrm{n}-1)$ possible pairings, one between each observation and the $(n-1)$

remaining observations; each observation always has a correlation of one with itself, and hence these n self-pairings are of little or no interest in terms of correlation. One relevant question asks whether or not an ordering exists that differentiates between two subsets of these $n(n-1)$ pairings such that the ordered subset contains directly correlated observations, whereas the unordered subset contains uncorrelated observations. For data linked to a map, its spatial ordering of attribute values virtually always yields a collection of correlated observations. Because the ordering involved is spatial, the
SA may be defined generically as the arrangement of attribute values on a map for some RV Y such that a map pattern becomes conspicuous by visual inspection. More specifically, positive SA (PSA)-overwhelmingly the most commonly observed type of SA-may be defined as the tendency for similar $Y$ values to cluster on a map. In other words, larger values of $Y$ tend to be surrounded by larger values of $Y$, intermediate values of $Y$ tend to be surrounded by intermediate values of $Y$, and smaller values of $Y$ tend to be surrounded by smaller values of Y. In contrast, NSA-a rarely observed type of SA-may be defined as the tendency for dissimilar $Y$ values to cluster on a map. In other words, larger values of $Y$ tend to be surrounded by smaller values of $Y$, intermediate values of $Y$ tend to be surrounded by intermediate values of $Y$, and smaller values of Y tend to be surrounded by larger values of Y. The absence of $\mathrm{SA}$ indicates a lack of map pattern and a haphazard mixture of attribute values across a map.

统计代写|回归分析作业代写Regression Analysis代考|A mathematical formularization of the first law

The preceding definition of $\mathrm{SA}$ indicates that this concept exists because orderliness, (map) pattern, and systematic concentration, rather than randomness, epitomize real-world geospatial phenomena. Tobler’s $(1969$, P. 7) First Law of Geography captures this notion: “everything is related to everything else, but near things are more related than distant things.” In 2004 the Annals of the American Association of Geographers published commentaries by six prominent geographers (Sui, Barnes, Miller, Phillips, Smith, and Goodchild), together with a reply by Tobler (vol. 94: pp. $269-310$ ) about this notion. Subsequent quantitative SA measurements (e.g., see Section 1.1.3) are mathematical abstractions of this empirical rule.

统计代写|回归分析作业代写Regression Analysis代考|Quantifying spatial relationships

A spatial weights matrix (SWM) is an n-by-n nonnegative (i.e., all of its entries are zero or positive) matrix, say C, describing the geographic relationship structure latent in a georeferenced dataset containing n observations (areal units or point locations in the case of georeferenced data), and has $\mathrm{n}(\mathrm{n}-1) / 2$ potential pairwise, symmetric relationship designations; without invoking symmetry, it has $n(n-1)$ potential relationship designations. Classical statistics assumes that these pairwise relationship designations do not exist (i.e., observation independence). Time-series analyses assume that $(n-1)$ of these pairwise relationship designations are nonzero and asymmetric (dependence is one-directional in time), with perhaps several additional relationship designations to capture seasonality effects. Spatial data mostly assume that between $n-1$ and $3(n-2)$ of these pairwise relationship designations are nonzero and symmetric, with asymmetric relationships usually specified from symmetric ones. The relationship definition rule (often called the neighbor or adjacency rule) is that correlation between attribute values exists for areal unit polygons sharing a common nonzero length boundary (i.e., the rook definition, using a chess move analogy). One extension of this definition is to nonzero length (i.e., point contacts) shared boundaries (i.e., the queen definition, using a chess move analogy). This latter extension tends to increase the number of designated pairwise correlations for administrative polygon surface partitionings by roughly $10 \%$; its asymptotic upper bound is a doubling of pairwise relationships (i.e., the regular square lattice case) for this near-planar situation, which still constitutes a very small percentage of the $n(n-1) / 2$ possible relationshipr. A third extension is to $k>1$ nearest neighbors, which fails to guarantee a connected dual graph structure and for which $\mathrm{k}$ is sufficiently small that it still constitutes a very small percentage of the $n(n-1)$ possible relationships. In all of these specifications of matrix $C$, if areal units $i$ and $j$ are designated polygons/locations with correlated attribute values, then $c_{i j}=1$; otherwise, $c_{i j}=0$. Frequently, matrix $C$ is converted to its often asymmetric row-standardized counterpart, matrix $W$, for which $w_{i j}=c_{i j} / \sum_{j=1}^{n} c_{i j} ; \sum_{j=1}^{n} w_{i j}=1$.

Yet another specification involves inverse distance (i.e., power or negative exponential) between polygon centroids or other points of privilege (e.g., administrative centers, such as capital cities or county seats) within areal unit polygons; these interpoint distances almost always are standardized (i.e., converted to matrix W), perhaps with a carefully chosen power or exponent parameter that essentially equates them to their shared common

boundary topological structure counterpart. Tiefelsdorf, Griffith, and Boots (1999) discuss other schemes defining a SWM that lies between matrices $\mathbf{C}$ and W.

These nearest neighbor and distance-based specifications allow spatial researchers to posit geographic relationship structures for nonpolygon point observations. By generating Thiessen polygon surface partitionings, these researchers also can posit geographic relationships based upon common boundary rules. Eigenvalues of matrices $C$ and $W$, a topic treated in a number of ensuing sections, furnish a quantitative gauge for comparing competing SWMs.

The purpose of a SWM is to define the set of directly correlated observations within a $R V$, enabling the quantification of $S A$ for a georeferenced attribute. It captures the geometric arrangement of attribute values on a map, often in topological terms.

统计代写|回归分析作业代写Regression Analysis代考|Spatial autocorrelation

回归分析代写

统计代写|回归分析作业代写Regression Analysis代考|Defining SA

非零相关性的存在导致一个R在, 是, 在一对依赖于另一个R在, X. 其描绘正相关的全局趋势是对于较大的值X和是倾向于重合，对于中间值X和是倾向于重合，并且对于较小的值X和是趋于一致；的值X与它们的相应值成正比是. 对于间接（即负或反向）关系，较大的值X往往与较小的值一致是, 的中间值X和是倾向于重合，并且较小的值X往往与较大的值一致是; 的值X与它们的相应值成反比是. 随机关系的值为X和是根据它们的相对大小随意重合。

自相关将这种关系概念从两个 RV 转移到单个 RV；前缀 auto 表示自我。因此，n观察有n(n−1)可能的配对，在每个观察和(n−1)

剩余的观察；每个观察值总是与自身相关，因此这 n 个自配对在相关性方面几乎没有兴趣或没有兴趣。一个相关的问题是，是否存在区分这两个子集的排序n(n−1)配对使得有序子集包含直接相关的观察，而无序子集包含不相关的观察。对于链接到地图的数据，其属性值的空间排序实际上总是会产生一组相关的观察结果。因为所涉及的排序是空间的，所以
SA 可以一般地定义为一些 RV Y 的地图上的属性值的排列，使得地图图案通过视觉检查变得明显。更具体地说，阳性 SA（PSA）——绝大多数是最常见的 SA 类型——可以定义为相似的趋势是在地图上聚类的值。换句话说，较大的值是往往被较大的值包围是, 的中间值是往往被中间值包围是, 和较小的值是倾向于被较小的 Y 值包围。相比之下，NSA（一种很少观察到的 SA 类型）可以定义为不相似的趋势是在地图上聚类的值。换句话说，较大的值是往往被较小的值包围是, 的中间值是往往被中间值包围是, 较小的 Y 值往往被较大的 Y 值包围。小号一种表示缺乏地图模式和地图上属性值的随意混合。

统计代写|回归分析作业代写Regression Analysis代考|A mathematical formularization of the first law

前面的定义小号一种表明这个概念的存在是因为有序、（地图）模式和系统集中，而不是随机性，是现实世界地理空间现象的缩影。托布勒(1969, P. 7) 地理学第一定律抓住了这个概念：“一切都与其他一切相关，但近处的事物比远处的事物更相关。” 2004 年，美国地理学家协会年鉴发表了六位著名地理学家（Sui、Barnes、Miller、Phillips、Smith 和 Goodchild）的评论，以及 Tobler 的回复（第 94 卷：pp.269−310) 关于这个概念。随后的定量 SA 测量（例如，参见第 1.1.3 节）是该经验规则的数学抽象。

统计代写|回归分析作业代写Regression Analysis代考|Quantifying spatial relationships

空间权重矩阵 (SWM) 是一个 n×n 非负（即其所有条目均为零或正）矩阵，例如 C，描述了包含 n 个观测值（面积单位或点）的地理参考数据集中潜在的地理关系结构在地理参考数据的情况下的位置），并且有n(n−1)/2潜在的成对对称关系名称；在不调用对称的情况下，它有n(n−1)潜在的关系名称。经典统计假设这些成对关系名称不存在（即观察独立性）。时间序列分析假设(n−1)这些成对的关系指定是非零和不对称的（依赖性在时间上是单向的），可能还有几个额外的关系指定来捕捉季节性影响。空间数据大多假设n−1和3(n−2)这些成对关系的指定是非零和对称的，不对称关系通常由对称关系指定。关系定义规则（通常称为邻居或邻接规则）是属性值之间的相关性存在于共享公共非零长度边界的区域单元多边形（即，使用国际象棋移动类比的车定义）。该定义的一个扩展是非零长度（即点接触）共享边界（即，皇后定义，使用国际象棋移动类比）。后一种扩展倾向于将行政多边形表面分区的指定成对相关性的数量大致增加10%; 对于这种接近平面的情况，它的渐近上界是成对关系的两倍（即，正方格子的情况），它仍然占n(n−1)/2可能的关系者。第三个扩展是ķ>1最近的邻居，它不能保证一个连通的对偶图结构，并且ķ足够小，以至于它仍然只占很小的百分比n(n−1)可能的关系。在所有这些规格的矩阵中C, 如果是面积单位一世和j是具有相关属性值的指定多边形/位置，然后C一世j=1; 除此以外，C一世j=0. 通常，矩阵C被转换为其通常不对称的行标准化对应物，矩阵在, 为此在一世j=C一世j/∑j=1nC一世j;∑j=1n在一世j=1.

又一个规范涉及区域单元多边形内多边形质心或其他特权点（例如，行政中心，如首都或县城）之间的反距离（即幂或负指数）；这些点间距离几乎总是标准化的（即，转换为矩阵 W），可能使用精心选择的幂或指数参数，基本上将它们等同于它们共享的公共

边界拓扑结构对应物。Tiefelsdorf、Griffith 和 Boots (1999) 讨论了定义位于矩阵之间的 SWM 的其他方案C和W。

这些最近邻和基于距离的规范允许空间研究人员为非多边形点观测设定地理关系结构。通过生成泰森多边形表面分区，这些研究人员还可以根据共同的边界规则确定地理关系。矩阵的特征值C和在，在随后的许多部分中处理的主题，提供了一个定量标准，用于比较竞争的 SWM。

SWM 的目的是定义一组直接相关的观测值R在, 使量化小号一种对于地理参考属性。它通常以拓扑术语捕获地图上属性值的几何排列。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写