## 商科代写|计量经济学代写Econometrics代考|Best 27

statistics-lab™ 为您的留学生涯保驾护航 在代写计量经济学Econometrics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。我们的专家在代写计量经济学Econometrics代写方面经验极为丰富，各种代写计量经济学Econometrics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• 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

## 商科代写|计量经济学代写Econometrics代考|Formal Tests for Serial Correlation

The Durbin-Watson (DW) test provides a formal test in which the null hypothesis is that the equation errors are serially uncorrelated and the alternative is that they follow a first-order autocorrelation process. This test was first introduced by Durbin and Watson in two papers published in Biometrika in 1950 and 1951 [Durbin1950] and [Durbin1951]. It is a standard part of the regression output for most econometrics packages. The DW test builds on a previous test developed by Von Neumann [VonNeumann1941] who developed a test for autocorrelation in a series of random variables with the null that the variables are independent random numbers. Unfortunately, this is not suitable when the series under examination comprises regression residuals, which are not independent by construction. Although Von Neumann’s statistic has a relatively simple distribution, that is, the standard normal distribution, Durbin and Watson showed that the distribution of their test statistic was necessarily more complex. The nature of the test statistic means that it is not possible to derive unique critical values for a test of the null of no autocorrelation against the alternative of first-order autocorrelation. However, they did demonstrate that the critical values for their test were bounded and were able to tabulate the bounds for small sample sizes.
The DW test is concerned with a specific form of serial correlation, that is, first-order autocorrelation but is arguably sensitive to other forms. Consider the following regression model with an error that follows an AR process of order one:
\begin{aligned} &Y_{t}=\beta X_{t}+u_{t} \ &u_{t}=\rho u_{t-1}+\varepsilon_{t} . \end{aligned}
Taking the residuals from an OLS regression of $Y$ on $X$, we can construct the test statistic
$$D W=\sum_{t=2}^{T}\left(\hat{u}{t}-\hat{u}{t-1}\right)^{2} / \sum_{t=1}^{T} \hat{u}_{t}^{2} .$$

## 商科代写|计量经济学代写Econometrics代考|DEALING WITH SERIAL CORRELATION

If serial correlation is present, then there are several ways to deal with the issue. Of course, the priority is to identify the nature, and hopefully the cause, of the serial correlation. If the root cause of the problem is the omission of a relevant variable from the model, then the natural solution is to include that variable. If it is determined that modeling of the serial correlation process is appropriate, then we have several different methods available for the estimation of such models by adjusting for the presence of serially correlation errors. It should be noted that mechanical adjustments, of the type we will describe in this section, are potentially dangerous. This process has been much criticized on the grounds that there is a risk that these methods disguise an underlying problem rather than dealing with it. McGuirk and Spanos [McGuirk2009] are particularly critical of mechanical adjustments to deal with autocorrelated arguments. In this paper, they show that unless we can assume that the regress and does not Granger-cause the regressors, adjusting for autocorrelation means that least squares yield biased and inconsistent estimates. However, these methods are still used and reported in applied work and it is therefore important that we consider how they work.

The first method we will consider is that of Cochrane-Orcutt estimation. This uses an iterative algorithm proposed by Cochrane and Orcutt [Cochrane1949] in which we use the structure of the problem to separate out the estimation of the behavioral parameters of the main equation from those of the AR process that describes the errors. Let us consider the case of an $\mathrm{AR}(1)$ error process as an example. Suppose we wish to estimate a model of the form (5.6). The two equations can be combined to give a single equation of the form
$$Y_{t}-\rho Y_{t-1}=\beta\left(X_{t}-\rho X_{t-1}\right)+\varepsilon_{t},$$
that is, an equation in “quasi-differences” of the data. If $\rho$ was known, then it would be straightforward to construct these quasi-differences and estimate the behavioral parameter $\beta$ by least squares. In the absence of such knowledge, we make a guess at $\rho$ and construct an estimate of $\beta$ on this basis. We then generate the residuals $\hat{u}{t}=Y{t}-\beta X_{t}$ on this basis and calculate an estimate of $\rho$ of the form $\hat{\rho}=\sum_{t=2}^{T} \hat{u}{t} \hat{u}{t-1} / \sum_{t=1}^{T} \hat{u}_{t}^{2}$. If, by some lucky chance, this estimate coincides with our assumption, then we stop. Otherwise, we use our estimate to recalculate the quasi-differences, reestimate $\beta$, and continue until our estimates of $\beta$ and $p$ converge. If a solution exists, then this provides a robust algorithm for estimation.

## 商科代写|计量经济学代写Econometrics代考|Formal Tests for Serial Correlation

Durbin-Watson (DW) 检验提供了一种形式检验，其中零假设是方程误差是序列不相关的，而另一种方法是它们 遵循一阶自相关过程。该测试由 Durbin 和 Watson 在 1950 年和 1951 年在 Biometrika 发表的两篇论文 [Durbin1950] 和 [Durbin1951] 中首次引入。它是大多数计量经济学软件包回归输出的标准部分。DW 测试建立 在 Von Neumann [VonNeumann1941] 开发的先前测试的基础上，该测试开发了一系列随机变量的自相关测 试，其中变量为独立随机数。不幸的是，当检查的序列包含回归残差时，这不适合，这些回归残差在构造上不是 独立的。尽管冯诺依曼的统计量具有相对简单的分布，即标准正态分布，但 Durbin 和 Watson 表明，他们的检 验统计量的分布必然更复杂。检验统计量的性质意味着不可能为无自相关的零点与一阶自相关的备选方案的检验 推导出唯一的临界值。然而，他们确实证明了他们测试的临界值是有界的，并且能够将小样本的界限制表。检验 统计量的性质意味着不可能为无自相关的零点与一阶自相关的备选方案的检验推导出唯一的临界值。然而，他们 确实证明了他们测试的临界值是有界的，并且能够将小样本的界限制表。检验统计量的性质意味着不可能为无自 相关的零点与一阶自相关的备选方案的检验推导出唯一的临界值。然而，他们确实证明了他们测试的临界值是有 界的，并且能够将小样本的界限制表。

DW 检验关注特定形式的序列相关，即一阶自相关，但可以说对其他形式敏感。考虑以下回归模型，其误差遵循 一阶 AR 过程:
$$Y_{t}=\beta X_{t}+u_{t} \quad u_{t}=\rho u_{t-1}+\varepsilon_{t} .$$

$$D W=\sum_{t=2}^{T}(\hat{u} t-\hat{u} t-1)^{2} / \sum_{t=1}^{T} \hat{u}_{t}^{2} .$$

## 商科代写|计量经济学代写Econometrics代考|DEALING WITH SERIAL CORRELATION

$$Y_{t}-\rho Y_{t-1}=\beta\left(X_{t}-\rho X_{t-1}\right)+\varepsilon_{t},$$

## 有限元方法代写

tatistics-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。

## 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。

## 商科代写|计量经济学代写Econometrics代考|Best 22

statistics-lab™ 为您的留学生涯保驾护航 在代写计量经济学Econometrics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。我们的专家在代写计量经济学Econometrics代写方面经验极为丰富，各种代写计量经济学Econometrics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• 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

## 商科代写|计量经济学代写Econometrics代考|DETECTION OF SERIAL CORRELATION

Since serial correlation of the errors has been shown to have important implications for our interpretation of regression results, it becomes important to develop tests for whether it is present in the models we estimate. It will be helpful to have an example in mind as we develop such tests. Consider the following estimated consumption function for the US economy based on annual data from 1970 to $2019 .$
$\ln \left(C_{t}\right)=\underset{(0.0466)}{-0.2898}+\underset{(0.0052)}{1.0174} \ln \left(Y D_{t}\right)+\hat{u}{t}$ $R^{2}=0.9987 \quad \hat{\sigma}{u}=0.0154 \quad T=50$
$D W=0.5389$,
where $C$ is total consumers’ expenditure and $Y D$ is real personal disposable income. Both variables are measured in millions of dollars at 2012 prices.
On first inspection, this equation appears to have reasonable properties. The slope coefficient is statistically significantly different from zero and the coefficient of determination indicates a good fit. In this case, however, it is more interesting to test the null hypothesis that the slope coefficient is equal to 1 . This is because the slope coefficient in this relationship measures the income elasticity of consumption expenditure. However, this null hypothesis is also rejected by our model. The $t$ statistic for this test is $(1.0174-1) / 0.0052=3.35$ which leads us to reject the null at the $5 \%$ level. This conclusion is, however, may be unreliable if the errors in this model are serially correlated. Therefore, in order to assess the robustness of our estimates of the model parameters, we need to test for the presence of serial correlation in the residuals $\hat{u}$ from equation (5.18).

## 商科代写|计量经济学代写Econometrics代考|Informal Tests for Serial Correlation

We can look for serial correlation informally by simply inspecting a plot of the residuals. If runs of positive or negative residuals are obvious, then this is a sign that serial correlation is present. For example, Figure $5.2$ shows the residuals for our consumption function equation and it is obvious that there are periods during which the residuals are consistently either positive or negative. This is a clear indication that the equation suffers from serial correlation. There are, however, forms of serial correlation, such as moving average errors, which are not so easily detected. Therefore, it is important to develop more formal tests as well as procedures for identifying the specific form of serial correlation that is relevant for this equation.

The correlogram 1 provides a more formal statistical method for the investigation of serial correlation. The correlogram is a table, or plot, of the sample autocorrelations of the regression residuals. The sample autocorrelations are defined in equation (5.19), and Figure $5.3$ gives both a table and a graph of the autocorrelations of the residuals from equation (5.18).
$$\hat{\rho}{k}=\sum{t=k+1}^{T} \hat{u}{t} \hat{u}{t-k} / \sum_{t=1}^{T} \hat{u}_{t^{2}}^{2} .$$

## 商科代写|计量经济学代写Econometrics代考|Informal Tests for Serial Correlation

$$\hat{\rho} k=\sum t=k+1^{T} \hat{u} t \hat{u} t-k / \sum_{t=1}^{T} \hat{u}_{t^{2}}^{2} .$$

## 有限元方法代写

tatistics-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。

## 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。

## 商科代写|计量经济学代写Econometrics代考|Find 2022

statistics-lab™ 为您的留学生涯保驾护航 在代写计量经济学Econometrics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。我们的专家在代写计量经济学Econometrics代写方面经验极为丰富，各种代写计量经济学Econometrics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• 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

## 商科代写|计量经济学代写Econometrics代考|CAUSES OF SERIAL CORRELATION

Consider a regression equation of the standard form $Y_{t}=\beta X_{t}+u_{t}$. We assume a model in mean deviation form to simplify the notation and the discussion. The errors of this model are said to be serially correlated if $E\left(u_{t} u_{t-k}\right) \neq 0$ for some $k \neq 0$. A natural question is why the errors might be correlated in this way? For the moment, we will simply assume that this is an intrinsic property of the data. That is, we assume that shocks to the equation are not random drawings from a distribution but instead depend upon their own past values. An alternative would be to assume that correlation in the errors arises because the model is misspecified in some way. However, this would complicate much of the discussion and we will avoid this assumption for the moment, on the understanding that it will be relaxed later.

There are many different forms that serial correlation might take. For example, the errors might follow a first-order autoregressive (AR) process. This would mean that the error process could be described by an equation of the form $u_{t}=\rho u_{t-1}+\varepsilon_{t}$, where $\varepsilon_{t}$, is a truly random disturbance and $\rho \neq 0$. This is a very common and important case, but it is not the only form that serial correlation can take. An alternative is where the error term in the equation is an average over several time periods of the random disturbance $\varepsilon_{t}$. For example, we might have a first-order moving average process of the form $u_{t}=\varepsilon_{t}+\lambda \varepsilon_{t-1}$. Both error processes are said to be serially correlated but each produces different implications and problems for the modeler. However, in both cases, the problem of dealing with serial correlation is simplified because of the assumption that it is an intrinsic feature of the error themselves, that is, the problem is one of error dynamics. A more realistic conclusion might be that the errors are serially correlated because of some fundamental misspecification in the original equation.

## 商科代写|计量经济学代写Econometrics代考|CONSEQUENCES OF SERIAL CORRELATION

Now that we have established some of the reasons why serial correlation may arise in regression models, let us consider the implications for least squares regression analysis. Suppose we have a model in which the errors follow a first-order AR process as set out in (5.6)
\begin{aligned} &Y_{t}=\beta X_{t}+u_{t} \ &u_{t}=\rho u_{t-1}+\varepsilon_{t}, \end{aligned}
where $\varepsilon_{t}, t=1, \ldots, T$ are independent, identically distributed random disturbances with mean zero and constant variance. As we have seen, this is not the only possible type of serial correlation which may arise, but the results we derive for this model apply more generally to other forms of serial correlation.

The AR process defined in (5.6) can be written in moving average form. Using the method of backward substitution, we have
$$u_{t}=\varepsilon_{t}+\rho \varepsilon_{t-1}+\rho^{2} \varepsilon_{t-2} \ldots=\sum_{j=0}^{\infty} \rho^{j} \varepsilon_{t-j} .$$
This is an infinite moving average process. Providing $|\rho|<1$, then the sequence defined in (5.7) will converge, in the sense that it will have a finite variance. To see this note that
$$E\left(u_{t}^{2}\right)=\sum_{j=0}^{\infty} \rho^{2 j} E\left(\varepsilon_{t-j}^{2}\right)=\sum_{j=0}^{\mu_{j}} \rho^{2 j} \sigma_{\varepsilon}^{2}=\frac{\sigma_{\varepsilon}^{2}}{1-\rho^{2}}$$
Therefore, for the variance of the error term to be finite and positive, we need $|\rho|<1$. If this condition holds, then the process is said to be weakly stationary and it can be shown that a general feature of stationary, finite AR processes is that they can be written as infinite moving average processes. Moreover, since $E\left(\varepsilon_{t-j}\right)=0$ for all values of $j$, it follows that $E\left(u_{t}\right)=0$. This is a useful property because we have already seen that the expected value of the OLS estimator can be written as follows: $E(\hat{\beta})=\beta+\sum_{t=1}^{T} X_{t} E\left(u_{t}\right) / \sum_{t=1}^{T} X_{t}^{2}$. It therefore follows that $E(\hat{\beta})=\beta$ and that the OLS estimator is unbiased even when the errors are serially correlated.

## 商科代写|计量经济学代写Econometrics代考|CONSEQUENCES OF SERIAL CORRELATION

$$Y_{t}=\beta X_{t}+u_{t} \quad u_{t}=\rho u_{t-1}+\varepsilon_{t},$$

(5.6) 中定义的 AR 过程可以写成移动平均形式。使用向后替换的方法，我们有
$$u_{t}=\varepsilon_{t}+\rho \varepsilon_{t-1}+\rho^{2} \varepsilon_{t-2} \ldots=\sum_{j=0}^{\infty} \rho^{j} \varepsilon_{t-j} .$$

$$E\left(u_{t}^{2}\right)=\sum_{j=0}^{\infty} \rho^{2 j} E\left(\varepsilon_{t-j}^{2}\right)=\sum_{j=0}^{\mu_{j}} \rho^{2 j} \sigma_{\varepsilon}^{2}=\frac{\sigma_{\varepsilon}^{2}}{1-\rho^{2}}$$

## 有限元方法代写

tatistics-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。

## 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。

## 商科代写|商业数学代写business mathematics代考|ETF5970

statistics-lab™ 为您的留学生涯保驾护航 在代写商业数学business mathematics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。我们的专家在代写商业数学business mathematics代写方面经验极为丰富，各种代写商业数学business mathematics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• 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

## 商科代写|商业数学代写business mathematics代考|Probability and Expected Value

First, let us discuss games of chance. Games of chance include, but are not limited to, games involving flipping coin, rolling dice, drawing cards from a deck, spinning a wheel, and such. Suppose you are flipping a coin with a friend. If you both flip the same, both heads or both tails, you win $\$ 1$. If you flip a head and a tail each, you lose$\$1$. If you play this game with this bet 100 times over the course of the evening, how much do you expect to win? Or lose? To answer such questions, we need two concepts: the probability of an event and the expected value of a random variable.

In situations like this, it makes sense to count the number of times something occurs. An efficient way to do this is to use the frequency definition of the probability of an event. The probability of the event two heads or two tails is the number of ways we can achieve these results divided by the total number of possible outcomes. That is, we define both coins being flipped that land on both heads or both tails as a favorable event $A$. We can define event $A$ as the set of outcomes that include ${\mathrm{HH}, \mathrm{TT}}$.
Favorable outcomes are those that consist of ${\mathrm{HH}, \mathrm{TT}}$.
$$\begin{array}{r} \text { Probability of an event }=\frac{\text { Favorable outcomes }}{\text { Total outcomes }} \ \text { Probability of an event }{A}=\frac{\text { Number of outcomes of }{A}}{\text { Total outcomes }} \end{array}$$

Of course, the probability of an event (flip of a fair coin) must be equal or greater than zero, and equal to or less than 1. And the sum of the probabilities of all possible events must equal 1 . That is,
\begin{aligned} &0 \leq p_{i} \leq 1 \ &\sum_{i=1}^{n} p_{i}=1, i=1,2, \ldots, n \end{aligned}
We need to compute all the possible outcomes of flipping two coins, and then determine how many result in the same results defined by event $A$. A tree is useful for visualizing the outcomes. These outcomes constitute the sample space. On the first flip, the possible results are $\mathrm{H}$ or $\mathrm{T}$. And on the second flip, the same outcomes are still available. We assume that these events are equally likely to occur based on flipping and obtaining either a head or tail of each flip.

## 商科代写|商业数学代写business mathematics代考|Expected Value

First, we define a random variable as a rule that assigns a number to every outcome of a sample.

We use $E[X]$, which is stated as the expected value of $X$. We define $E[X]$ as follows:
Expected value, $E[X]$, is the mean or average value.
Further, we provide the following two formulas: in the discrete case, $E[X]=\sum_{i=1}^{n} x_{i} p\left(x_{i}\right)$ and in the continuous case, $E[X]=\int_{-\infty}^{+\infty} x * f(x) d x$.

There are numerous ways to calculate the average value. We present a few common methods that you could use in decision theory.

If you had 2 quiz grades, an 82 and a 98 , almost intuitively you would add the two numbers and divide by 2 , giving an average of 90 .

Average scores: Two scores that were earned were 82 and 98 . Compute the average.
$$E[X]=\frac{(82+98)}{2}=90$$
If after 5 quizzes, you had three 82 s and two 98 s, you would add them and divide by $5 .$
$$\text { Average }=\frac{3(82)+2(98)}{5}=88.4$$
Rearranging the terms, we obtain
$$\text { Average }=\frac{3}{5}(82)+\frac{2}{5}(98)$$
In this form, we have two payoffs, 82 and 98 , each multiplied by the weights, $3 / 5$ and $2 / 5$. This is analogous to the definition of expected value.

Suppose a game has outcomes $a_{1}, a_{2}, \ldots, a_{n}$, each with a payoff $w_{1}, w_{2}, \ldots, w_{n}$ and a corresponding probability $p_{1}, p_{2}, \ldots, p_{n}$ where $p_{1}+p_{2}+\ldots+p_{n}=1$ and $0 \leq p_{i} \leq 1$, then the quantity
$$E=w_{1} p_{1}+w_{1} p_{2}+\ldots+w_{1} p_{n}$$
is the expected value of the game. Note that expected value is analogous to weighted average, but the weights must be probabilities $\left(0 \leq p_{i} \leq 1\right)$ and the weights must sum to 1 .

## 商科代写|商业数学代写business mathematics代考|Probability and Expected Value

Probability of an event $=\frac{\text { Favorable outcomes }}{\text { Total outcomes }}$ Probability of an event $A=\frac{\text { Number of outcomes of } A}{\text { Total outcomes }}$

$$0 \leq p_{i} \leq 1 \quad \sum_{i=1}^{n} p_{i}=1, i=1,2, \ldots, n$$

## 商科代写|商业数学代写business mathematics代考|Expected Value

$$E[X]=\frac{(82+98)}{2}=90$$

$$\text { Average }=\frac{3(82)+2(98)}{5}=88.4$$

$$\text { Average }=\frac{3}{5}(82)+\frac{2}{5}(98)$$

$$E=w_{1} p_{1}+w_{1} p_{2}+\ldots+w_{1} p_{n}$$

## 有限元方法代写

tatistics-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。

## 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。

## 商科代写|商业数学代写business mathematics代考|MATH1901D

statistics-lab™ 为您的留学生涯保驾护航 在代写商业数学business mathematics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。我们的专家在代写商业数学business mathematics代写方面经验极为丰富，各种代写商业数学business mathematics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• 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

## 商科代写|商业数学代写business mathematics代考|Mathematical Modeling for Business Analytics as a Process

We will illustrate some mathematical models that describe change in the real world. We will solve some of these models and will analyze how good our resulting mathematical explanations and predictions are in context of the problem. The solution techniques that we employ take advantage of certain characteristics that the various models enjoy as realized through the formulation of the model.

When we observe change, we are often interested in understanding or explaining why or how a particular change occurs. Maybe we need or want to analyze the effects under different conditions or perhaps to predict what could happen in the future. Consider the firing of a weapon system or the shooting of a ball from a catapult as shown in Figure 1.3. Understanding how the system behaves in different environments under differing weather or operators, or predicting how well it hits the targets are all of interest. For the catapult, the critical elements of the ball, the tension, and angle of the firing arm are found as important elements (Fox, 2013b). For our purposes, we will consider a mathematical model to be a mathematical construct that is designed to study a particular real-world system or behavior (Giordano et al., 2014). The model allows us to use mathematical operations to reach mathematical conclusions about the model as illustrated in Figure 1.4. It is the arrow going from real-world system and observations to the mathematical model using the assumptions, variables, and formulations that are critical in the process.

We define a system as a set of objects joined by some regular interaction or interdependence in order for the complete system to work together. Think of a larger business with many companies that work independently and interact together to make the business prosper. Other examples might include a bass and trout population living in a lake, a communication, cable TV, or weather satellite orbiting the earth, delivering Amazon Prime packages, U.S. postal service mail or packages, locations of emergency services or computer terminals, or large companies’ online customer buying systems. The person modeling is interested in understanding how a system works, what causes change in a system, and the sensitivity of the system to change. Understanding all these elements will help in building an adequate model to replicate reality. The person modeling is also interested in predicting what changes might occur and when these changes might occur.

## 商科代写|商业数学代写business mathematics代考|Steps in Model Construction

An outline is presented as a procedure to help construct mathematical models. In the next section, we will illustrate this procedure with a few examples. We suggest a nine-step process.

These nine steps are summarized in Figure 1.6. These steps act as a guide for thinking about the problem and getting started in the modeling process. We choose these steps from the compilation of steps by other authors listed in additional readings and put them together in these nine steps.

We illustrate the process through an example. Consider building a model where we want to identify the spread of a contagious disease.
Step 1: Understand the decision to be made, the question to be asked, or the problem to be solved.

Understanding the decision is the same as identifying the problem to be solved. Identifying the problem to study is usually difficult.

In real life, no one walks up to you and hands you an equation to be solved. Usually, it is a comment like “we need to make more money” or “we need to improve our efficiency.” Perhaps, we need to make better decisions or we need all our units that are not $100 \%$ efficient to become more efficient. We need to be precise in our formulation of the mathematics to actually describe the situation that we need to solve. In our example, we want to identify the spread of a contagious disease to determine how fast it will spread within our region. Perhaps, we will want to use the model to answer the following questions:

1. How long will it take until one thousand people get the disease?
2. What actions may be taken to slow or eradicate the disease?
Step 2: Make simplifying assumptions.
Giordano et al. (2014, pp. 62-65) described this well. Again, we suggest starting by brain storming the situation. Make a list of as many factors, or variables, as you can. Now, we realize that we usually cannot capture all these factors influencing a problem in our initial model. The task now is simplified by reducing the number of factors under consideration. We do this by making simplifying assumptions about the factors, such as holding certain factors as constants or ignoring some in the initial modeling phase. We might then examine to see if relationships exist between the remaining factors (or variables). Assuming simple relationships might reduce the complexity of the problem. Once you have a shorter list of variables, classify them as independent variables, dependent variables, or neither.

In our example, we assume we know the type of disease, how it is spread, the number of susceptible people within our region, and what type of medicine is needed to combat the disease. Perhaps, we assume that we know the size of population and the approximate number susceptible to getting the disease.

## 商科代写|商业数学代写business mathematics代考|Steps in Model Construction

1. 一千人得这种病需要多长时间？
2. 可以采取哪些行动来减缓或根除这种疾病？
第 2 步：做出简化假设。
佐丹奴等人。(2014, pp. 62-65) 很好地描述了这一点。同样，我们建议从头脑风暴开始。尽可能多地列出因素或变量。现在，我们意识到我们通常无法在初始模型中捕获影响问题的所有这些因素。现在通过减少所考虑因素的数量来简化任务。我们通过简化对因素的假设来做到这一点，例如将某些因素保持为常数或在初始建模阶段忽略一些因素。然后我们可能会检查其余因素（或变量）之间是否存在关系。假设简单的关系可能会降低问题的复杂性。一旦你有一个较短的变量列表，将它们分类为自变量、因变量或两者都不是。

## 有限元方法代写

tatistics-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。

## 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。

## 商科代写|商业数学代写business mathematics代考|OPMT1110

statistics-lab™ 为您的留学生涯保驾护航 在代写商业数学business mathematics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。我们的专家在代写商业数学business mathematics代写方面经验极为丰富，各种代写商业数学business mathematics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• 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

## 商科代写|商业数学代写business mathematics代考|Overview and Process of Mathematical Modeling

Bender (2000, pp. 1-8) first introduced a process for modeling. He highlighted the following: formulate the model, outline the model, ask if it is useful, and test the model. Others have expanded this simple outlined process. Giordano et al. (2014, p. 64) presented a six-step process: identify the problem to be solved, make assumptions, solve the model, verify the model, implement the model, and maintain the model. Myer (2004, pp. 13-15) suggested some guidelines for modeling, including formulation, mathematical manipulation, and evaluation. Meerschaert (1999) developed a five-step process: ask the question, select the modeling approach, formulate the model, solve the model, and answer the question. Albright (2010) subscribed mostly to concepts and process described in previous editions of Giordano et al. (2014). Fox (2012, pp. 21-22) suggested an eight-step approach: understand the problem or question, make simplifying assumptions, define all variables, construct the model, solve and interpret the model, verify the model, consider the model’s strengths and weaknesses, and implement the model.
Most of these pioneers in modeling have suggested similar starts in understanding the problem or question to be answered and in making key assumptions to help enable the model to be built. We add the need for sensitivity analysis and model testing in this process to help ensure that we have a model that is performing correctly to answer the appropriate questions.

For example, student teams in the Mathematical Contest in Modeling were building models to determine the all-time best college sports coach. One team picked a coach who coached less than a year, went undefeated for the remaining part of the year, and won their bowl game. Thus, his season was a perfect season. Their algorithm picked this person as the all-time best coach. Sensitivity analysis and model testing could have shown the fallacy to their model.

Someplace between the defining of the variables and the assumptions, we begin to consider the model’s form and technique that might be used to solve the model. The list of techniques is boundless in mathematics, and we will not list them here. Suffice it to say that it might be good to initially decide among the forms: deterministic or stochastic for the model, linear or nonlinear for the relationship of the variables, and continuous or discrete.

## 商科代写|商业数学代写business mathematics代考|The Modeling Process

We introduce the process of modeling and examine many different scenarios in which mathematical modeling can play a role.

The art of mathematical modcling is learned through expericnce of building and solving models. Modelers must be creative, innovative, inquisitive, and willing to try new techniques as well as being able to refine their models, if necessary. A major step in the process is passing the common sense test for use of the model.
In its basic form, modeling consists of three steps:

1. Make assumptions
2. Do some math
3. Derive and interpret conclusions
To that end, one cannot question the mathematics and its solution, but one can always question the assumptions used.

To gain insight, we will consider one framework that will enable the modeler to address the largest number of problems. The key is that there is something changing for which we want to know the effects and the results of the effects. The problem might involve any system under analysis. The realworld system can be very simplistic or very complicated. This requires both types of real-world systems to be modeled with the same logical stepwise process.

Consider modeling an investment. Our first inclination is to use the equations about compound interest rates that we used in high school or college algebra. The compound interest formula calculates the value of a compound interest investment after ” $n$ ” interest periods.
$$A=P(1-i)^{n}$$

where:
$A$ is the amount after $n$ interest periods
$P$ is the principal, the amount invested at the start $i$ is the interest rate applying to each period $n$ is the number of interest periods

## 商科代写|商业数学代写business mathematics代考|Overview and Process of Mathematical Modeling

Bender (2000, pp. 1-8) 首先介绍了一种建模过程。他强调了以下几点：制定模型、概述模型、询问它是否有用以及测试模型。其他人已经扩展了这个简单的概述过程。佐丹奴等人。(2014, p. 64) 提出了一个六步过程：识别要解决的问题、做出假设、解决模型、验证模型、实施模型和维护模型。Myer (2004, pp. 13-15) 提出了一些建模指南，包括公式化、数学操作和评估。Meerschaert (1999) 制定了一个五步流程：提出问题、选择建模方法、制定模型、解决模型和回答问题。Albright (2010) 主要赞同 Giordano 等人先前版本中描述的概念和过程。（2014）。福克斯（2012 年，第

## 商科代写|商业数学代写business mathematics代考|The Modeling Process

1. 做出假设
2. 做一些数学
3. 推导和解释结论
为此，人们不能质疑数学及其解决方案，但人们总是可以质疑所使用的假设。

## 有限元方法代写

tatistics-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。

## 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。

## 商科代写|计量经济学代写Econometrics代考|ECON 2504

statistics-lab™ 为您的留学生涯保驾护航 在代写计量经济学Econometrics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。我们的专家在代写计量经济学Econometrics代写方面经验极为丰富，各种代写计量经济学Econometrics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• 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

## 商科代写|计量经济学代写Econometrics代考|Some Examples

Each of the loss functions that we discuss in this subsection corresponds to a machine learning algorithm, as thoroughly explained in Bühlmann and Hothorn (2007), Sect. 3. We refer to this article for more properties of these losses and for issues regarding their practical implementation.

• A first canonical example, in the regression setting, is to let $\psi(x, y)=(y-x)^{2}$ (squared error loss), which is 2 -strongly convex in its first argument (Assumption $\mathbf{A}{\mathbf{2}}$ ) and satisfies Assumption $\mathbf{A}{\mathbf{1}}$ as soon as $\mathbb{E} Y^{2}<\infty$. It also satisfies $\mathbf{A}{\mathbf{3}}^{\prime}$, with $\partial{x} \psi(x, y)=2(x-y)$ and $L=2$.
• Another example in regression is the loss $\psi(x, y)=|y-x|$ (absolute error loss), which is convex but not strongly convex in its first argument. Whenever strong convexity of the loss is required, a possible strategy is to regularize the objective via an $L^{2}$-type penalty, and take
$$\psi(x, y)=|y-x|+\gamma x^{2},$$
where $\gamma$ is a positive parameter (possibly function of the sample size $n$ in the empirical setting). This loss is (2 ) -strongly convex in $x$ and satisfies $\mathbf{A}{\mathbf{1}}$ and $\mathbf{A}{\mathbf{2}}$ whenever $\mathbb{E}|Y|<\infty$, with $\xi(x, y)=\operatorname{sgn}(x-y)+2 \gamma x$ (with $\operatorname{sgn}(u)=2 \mathbb{1}{[u>0]}-1$ for $u \neq 0$ and $\operatorname{sgn}(0)=0$ ). On the other hand, the function $\psi(\cdot, y)$ is not differentiable at $y$, so that the smoothness Assumption $\mathbf{A}{3}^{\prime}$ is not satisfied. However,
\begin{aligned} \mathbb{E}\left(\xi\left(x_{1}, Y\right)-\xi\left(x_{2}, Y\right) \mid X\right)=& \int\left(\operatorname{sgn}\left(x_{1}-y\right)-\operatorname{sgn}\left(x_{2}-y\right)\right) \mu_{Y \mid X}(\mathrm{~d} y)+2 \gamma\left(x_{1}-x_{2}\right) \ =& \mu_{Y \mid X}\left(\left(-\infty, x_{1}\right)\right)-\mu_{Y \mid X}\left(\left(-\infty, x_{2}\right)\right)+2 \gamma\left(x_{1}-x_{2}\right) \ &-\mu_{Y \mid X}\left(\left(x_{1}, \infty\right)\right)+\mu_{Y \mid X}\left(\left(x_{2}, \infty\right)\right) . \end{aligned}
Thus, if we assume for example that $\mu_{Y \mid X}$ has a density (with respect to the Lebesgue measure) bounded by $B$, then
$$\left|\mathbb{E}\left(\xi\left(x_{1}, Y\right)-\xi\left(x_{2}, Y\right) \mid X\right)\right| \leq 2(B+\gamma)\left|x_{1}-x_{2}\right|,$$
and Assumption $\mathbf{A}{3}$ is therefore satisfied. Of course, in the empirical setting, assuming that $\mu{Y \mid X}$ has a density precludes the use of the empirical measure $\mu_{n}$ for $\mu_{X, Y}$. A safe and simple alternative is to consider a smoothed version $\tilde{\mu}{n}$ of $\mu{n}$ (based,
• for example, on a kernel estimate; see Devroye and Györfi 1985), and to minimize the functional
• $$• C_{n}(F)=\int|y-F(x)| \tilde{\mu}{n}(\mathrm{~d} x, \mathrm{~d} y)+\gamma \int F(x)^{2} \tilde{\mu}{n}(\mathrm{~d} x) •$$
• over the linear combinations of functions in $\mathscr{F}$.

## 商科代写|计量经济学代写Econometrics代考|Two Algorithms

Let $\operatorname{lin}(\mathscr{F})$ be the set of all linear combinations of functions in $\mathscr{F}$, our collection of base predictors in $L^{2}\left(\mu_{X}\right)$. So, each $F \in \operatorname{lin}(\mathscr{F})$ has the form $F=\sum_{j=1}^{J} \beta_{j} f_{j}$. where $\left(\beta_{1}, \ldots, \beta_{J}\right) \in \mathbb{R}^{J}$ and $f_{1}, \ldots, f_{J}$ are elements of $\mathscr{F}$. Finding the infimum of the functional $C$ over lin $(\mathscr{F})$ is a challenging infinite-dimensional optimization problem, which requires an algorithm. The core idea of the gradient boosting approach is to greedily locate the infimum by producing a combination of base predictors via a gradient-descent-type algorithm in $L^{2}\left(\mu_{X}\right)$. Focusing on the basics, this can be achieved by two related yet different strategies, which we examine in greater

mathematical details below. Algorithm 1 appears in Mason et al. (2000), whereas Algorithm 2 is essentially due to Friedman (2001).

It is implicitly assumed throughout this paragraph that Assumption $\mathbf{A}{\mathbf{1}}$ is satisfied. We recall that under this assumption, the convex functional $C$ is locally bounded and therefore continuous. Thus, in particular, $$\inf {F \in \operatorname{lin}(\mathscr{F})} C(F)=\inf {F \in \operatorname{lin}(\mathscr{F})} C(F),$$ where $\varlimsup \overline{\operatorname{lin}(\mathscr{F})}$ is the closure of lin( $\mathscr{F})$ in $L^{2}\left(\mu{X}\right)$. Loosely speaking, looking for the infimum of $C$ over $\overline{\operatorname{lin}(\mathscr{F})}$ is the same as looking for the infimum of $C$ over all (finite) linear combinations of base functions in $\mathscr{F}$. We note in addition that if Assumption $\mathbf{A}{2}$ is satisfied, then there exists a unique function $\bar{F} \in \overline{\operatorname{lin}(\mathscr{F})}$ (which we call the boosting predictor) such that $$C(\bar{F})=\inf {F \in \operatorname{lin}(\mathscr{F})} C(F)$$
Algorithm 1. In this approach, we consider a class $\mathscr{F}$ of functions $f: \mathscr{X} \rightarrow \mathbb{R}$ such that $0 \in \mathscr{F}, f \in \mathscr{F} \Leftrightarrow-f \in \mathscr{F}$, and $|f|_{\mu_{X}}=1$ for $f \neq 0$. An example is the collection $\mathscr{F}$ of all $\pm$-binary trees in $\mathbb{R}^{d}$ using axis parallel cuts with $k$ terminal nodes (plus zero). Each nonzero $f \in \mathscr{F}$ takes the form $f=\sum_{j=1}^{k} \beta_{j} \mathbb{1}{A{j}}$, where $\left|\beta_{j}\right|=1$ and $A_{1}, \ldots, A_{k}$ is a tree-structured partition of $\mathrm{R}^{d}$ (Devroye et al. 1996, Chap. 20). The parameter $k$ is a measure of the tree complexity. For example, trees with $k=d+1$ are such that $\overline{\operatorname{lin}(\mathscr{F})}=L^{2}\left(\mu_{X}\right)$ (Breiman 2000). Thus, in this case,
$$\inf {F \in \operatorname{lin}(\mathscr{F})} C(F)=\inf {F \in L^{2}\left(\mu_{X}\right)} C(F)$$

## 商科代写|计量经济学代写Econometrics代考|Algorithm 1

The convergence of this algorithm rests upon the choice of the step size sequence $\left(w_{t}\right){t}$, which needs to be carefully specified. We take $w{0}>0$ arbitrarily and set
$$w_{t+1}=\min \left(w_{t},-(2 L)^{-1} \mathbb{E} \xi\left(F_{t}(X), Y\right) f_{t+1}(X)\right), \quad t \geq 0,$$
where $L$ is the Lipschitz constant of Assumption $\mathbf{A}{\mathbf{3}}$. Clearly, the sequence $\left(w{t}\right){t}$ is nonincreasing. It is also nonnegative. To see this, just note that, by definition, $$f{t+1} \in \arg \max {f \in \mathscr{F}}-\mathbb{E} \xi\left(F{t}(X), Y\right) f(X),$$
and thus, since $0 \in \mathscr{F},-\mathbb{E} \xi\left(F_{t}(X), Y\right) f_{t+1}(X) \geq 0$. The main result of this section is encapsulated in the following theorem.

Theorem 1 Assume that Assumptions $\mathbf{A}{\mathbf{1}}$ and $\mathbf{A}{\mathbf{3}}$ are satisfied, and let $\left(F_{t}\right){t}$ be defined by Algorithm 1 with $\left(w{t}\right){t}$ as in (8). Then $$\lim {t \rightarrow \infty} C\left(F_{t}\right)=\inf {F \in \operatorname{lin}(\mathscr{F})} C(F) .$$ Proof See Supplementary Material Document. Observe that Theorem 1 holds without Assumption $\mathbf{A}{2}$, i.e., there is no need here to assume that the function $\psi(x, y)$ is strongly convex in $x$. However, whenever Assumption $\mathbf{A}_{2}$ is satisfied, there exists as in (4) a unique boosting predictor $\bar{F} \in \overline{\operatorname{lin}(\mathscr{F})}$ such that $C(\bar{F})=\inf {F \in \operatorname{lin}(\mathscr{F})} C(F)$, and the theorem guarantees that $\lim {t \rightarrow \infty} C\left(F_{t}\right)=C(\bar{F})$

The proof of the theorem relies on the following lemma, which states that the sequence $\left(C\left(F_{t}\right)\right){t}$ is nonincreasing. Since $C(F)$ is nonnegative for all $F$, we concludê thât $C\left(F{t}\right) \downarrow \inf {k} C\left(F{k}\right)$ â $t \rightarrow \infty$. This is thé kêy argumént tó prové thé convergence of $C\left(F_{t}\right)$ toward inf $F \in \operatorname{lin}(\mathscr{F}) C(F)$.

## 商科代写|计量经济学代写Econometrics代考|Some Examples

• 第一个典型的例子，在回归设置中，是让 $\psi(x, y)=(y-x)^{2}$ (平方误差损失)，它的第一个参数是 2 – 强 凸 (假设 $\mathbf{A} 2$ ) 并满足假设 $\mathbf{A 1}$ 立刻 $\mathbb{E} Y^{2}<\infty$. 也满足 $\mathbf{A} \mathbf{3}^{\prime}$ ， 和 $\partial x \psi(x, y)=2(x-y)$ 和 $L=2$.
• 回归中的另一个例子是损失 $\psi(x, y)=|y-x|$ (绝对误差损失)，它是凸的，但在其第一个参数中不是强 凸的。每当需要损失的强凸性时，一种可能的策略是通过 $L^{2}$-型惩罚，并采取
$$\psi(x, y)=|y-x|+\gamma x^{2},$$
在哪里 $\gamma$ 是一个正参数 (可能是样本量的函数 $n$ 在经验设置中) 。这种损失是 (2) – 在 $x$ 并满足 $\mathbf{A} 1$ 和 $\mathbf{A} 2$ 每当 $\mathbb{E}|Y|<\infty$ ，和 $\xi(x, y)=\operatorname{sgn}(x-y)+2 \gamma x($ 和 $\operatorname{sgn}(u)=21[u>0]-1$ 为了 $u \neq 0$ 和 $\operatorname{sgn}(0)=0$ ) 。另一方面，函数 $\psi(\cdot, y)$ 不可微分 $y$, 使平滑假设 $\mathbf{A} 3^{\prime}$ 不满意。然而，
$$\mathbb{E}\left(\xi\left(x_{1}, Y\right)-\xi\left(x_{2}, Y\right) \mid X\right)=\int\left(\operatorname{sgn}\left(x_{1}-y\right)-\operatorname{sgn}\left(x_{2}-y\right)\right) \mu_{Y \mid X}(\mathrm{~d} y)+2 \gamma\left(x_{1}-x_{2}\right)=$$
因此，如果我们假设例如 $\mu_{Y \mid X}$ 有一个密度（相对于 Lebesgue 测度) 为界 $B$ ，然后
$$\left|\mathbb{E}\left(\xi\left(x_{1}, Y\right)-\xi\left(x_{2}, Y\right) \mid X\right)\right| \leq 2(B+\gamma)\left|x_{1}-x_{2}\right|,$$
和假设 $\mathbf{A} 3$ 因此感到满意。当然，在经验设置中，假设 $\mu Y \mid X$ 有一个密度排除了经验测量的使用 $\mu_{n}$ 为了 $\mu_{X, Y}$. 一个安全且简单的替代方案是考虑平滑版本 $\tilde{\mu} n$ 的 $\mu n$ (基于，
• 例如，在核估计上；参见 Devroye 和 Györfi 1985)，并最小化函数
• $\$ \$$• C_{n}(F)=|int |y F(x)| \backslash tilde {\backslash m u}{n}(\backslash \operatorname{mathrm}{\sim d} x, \mathrm {\sim d} y)+\backslash gamma \backslash int F(x)^{\wedge}{2} \backslash t \mathrm{~ i l d e {} (数学 {\sim d} x) • \\ • 在函数的线性组合上 \mathscr{F}. ## 商科代写|计量经济学代写Econometrics代考|Two Algorithms 让 \operatorname{lin}(\mathscr{F}) 是函数的所有线性组合的集合 \mathscr{F} ，我们收集的基础预测变量在 L^{2}\left(\mu_{X}\right). 所以，每个 F \in \operatorname{lin}(\mathscr{F}) 有形 式 F=\sum_{j=1}^{J} \beta_{j} f_{j}. 在哪里 \left(\beta_{1}, \ldots, \beta_{J}\right) \in \mathbb{R}^{J} 和 f_{1}, \ldots, f_{J} 是元素 \mathscr{F}. 寻找泛函的下确界 C 过林 (\mathscr{F}) 是一个具 有挑战性的无限维优化问题，需要一个算法。梯度提升方法的核心思想是通过梯度下降型算法生成基本预测变量的 组合来贪婪地定位下确界。 L^{2}\left(\mu_{X}\right). 专注于基础，这可以通过两种相关但不同的策略来实现，我们将在更大的 下面的数学细节。算法 1 出现在 Mason et al. (2000 年)，而算法 2 主要归功于 Friedman（2001 年)。 在本段中隐含地假设假设 \mathbf{A 1} 很满意。我们记得在这个假设下，凸泛函 C 是局部有界的，因此是连续的。因此，特 别是，$$
\inf F \in \operatorname{lin}(\mathscr{F}) C(F)=\inf F \in \operatorname{lin}(\mathscr{F}) C(F),
$$在哪里 \overline{\lim } \overline{\operatorname{lin}(\mathscr{F})} 是 \operatorname{lin}(\mathscr{F}) 在 L^{2}(\mu X). 松散地说，寻找下确界 C 超过 \overline{\operatorname{lin}(\mathscr{F}) \text { 和寻找下确界一样 } C \text { 基函数的所 } 有 (有限) 线性组合 \mathscr{F}. 我们还注意到，如果假设 \mathbf{A} 2 满足，则存在唯一函数 \bar{F} \in \overline{\operatorname{lin}(\mathscr{F})} (我们称之为提升预测 器) 使得$$
C(\bar{F})=\inf F \in \operatorname{lin}(\mathscr{F}) C(F)
$$算法 1. 在这种方法中，我们考虑一个类 \mathscr{F} 功能 f: \mathscr{X} \rightarrow \mathbb{R} 这样 0 \in \mathscr{F}, f \in \mathscr{F} \Leftrightarrow-f \in \mathscr{F} ，和 |f|{\mu{X}}=1 为了 f \neq 0. 一个例子是集合 \mathscr{F} 其中 \pm – 二叉树 \mathbb{R}^{d} 使用轴平行切割 k 终端节点 (加零) 。每个非零 f \in \mathscr{F} 采取形式 f=\sum_{j=1}^{k} \beta_{j} 1 A j ，在哪里 \left|\beta_{j}\right|=1 和 A_{1}, \ldots, A_{k} 是一个树形结构的分区 \mathrm{R}^{d} (Devroye 等人，1996 年，第 20 章) 。参数 k 是树复杂度的度量。例如，树与 k=d+1 是这样的 \overline{l i n}(\mathscr{F})=L^{2}\left(\mu_{X}\right) (布雷曼 2000) 。因 此，在这种情况下，$$
\inf F \in \operatorname{lin}(\mathscr{F}) C(F)=\inf F \in L^{2}\left(\mu_{X}\right) C(F)
$$## 商科代写|计量经济学代写Econometrics代考|Algorithm 1 该算法的收敛取决于步长序列的选择 \left(w_{t}\right) t, 这需要仔细指定。我们采取 w 0>0 任意设置$$
w_{t+1}=\min \left(w_{t},-(2 L)^{-1} \mathbb{E} \xi\left(F_{t}(X), Y\right) f_{t+1}(X)\right), \quad t \geq 0,
$$在哪里 L 是假设的 Lipschitz 常数 \mathbf{A 3}. 显然，序列 (w t) t 是非增加的。它也是非负的。要看到这一点，请注意，根 据定义，$$
f t+1 \in \arg \max f \in \mathscr{F}-\mathbb{E} \xi(F t(X), Y) f(X),
$$因此，由于 0 \in \mathscr{F},-\mathbb{E} \xi\left(F_{t}(X), Y\right) f_{t+1}(X) \geq 0. 本节的主要结果封装在以下定理中。 定理 1 假设假设 \mathbf{A} 1 和 \mathbf{A} 3 满意，让 \left(F_{t}\right) t 由算法 1 定义 (w t) t 如（8)。然后$$
\lim t \rightarrow \infty C\left(F_{t}\right)=\inf F \in \operatorname{lin}(\mathscr{F}) C(F) .
$$证明见补充材料文件。观察定理 1 在没有假设的情况下成立 \mathbf{A} 2 ，即这里不需要假设函数 \psi(x, y) 是强凸的 x. 然而， 每当假设 \mathbf{A}{2} 满足，如（4) 中存在一个唯一的提升预测器 \bar{F} \in \overline{\operatorname{lin}(\mathscr{F}) \text { 这样 } C(\bar{F})=\inf F \in \operatorname{lin}(\mathscr{F}) C(F) \text {, 该 } 定理保证 \lim t \rightarrow \infty C\left(F{t}\right)=C(\bar{F}) 定理的证明依赖于以下引理，它表明序列 \left(C\left(F_{t}\right)\right) t 是非增加的。自从 C(F) 对所有人都是非负的 F ，我们真的得 出结论 C(F t) \downarrow \inf k C(F k) 一个 t \rightarrow \infty. 这是证明收敛性的论证 C\left(F_{t}\right) 朝着inf F \in \operatorname{lin}(\mathscr{F}) C(F). 统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。 ## 金融工程代写 金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。 ## 非参数统计代写 非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。 ## 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。 术语 广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。 ## 有限元方法代写 有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。 有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。 tatistics-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。 ## 随机分析代写 随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。 ## 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。 ## 商科代写|计量经济学代写Econometrics代考|ECON 7204 如果你也在 怎样代写计量经济学Econometrics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。 计量经济学，对经济关系的统计和数学分析，通常作为经济预测的基础。这种信息有时被政府用来制定经济政策，也被私人企业用来帮助价格、库存和生产方面的决策。 statistics-lab™ 为您的留学生涯保驾护航 在代写计量经济学Econometrics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。我们的专家在代写计量经济学Econometrics代写方面经验极为丰富，各种代写计量经济学Econometrics相关的作业也就用不着说。 我们提供的计量经济学Econometrics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 高等概率论 • 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 ## 商科代写|计量经济学代写Econometrics代考|Simulation and Comparisons with Other Estimators In this section, we compare the LSE with the Simple Score Estimator (SSE), the Efficient Score Estimator (ESE), the Effective Dimension Reduction (EDR) estimate, the spline estimate, the MAVE estimate, and the EFM estimate. We take part in the simulation settings in Balabdaoui et al. (2019a), which means that we take the dimension d equal to 2 . Since the parameter belongs to the boundary of a circle in this case, we only have to determine a one-dimensional parameter. Using this fact, we use the parameterization \alpha=\left(\alpha_{1}, \alpha_{2}\right)=(\cos (\beta), \sin (\beta)) and determine the angle \beta by a golden section search for the SSE, ESE, and spline estimate. For EDR, we used the \mathrm{R} package edr: the method is discussed in Hristache et al. (2001). The spline method is described in Kuchibhotla and Patra (2020), and there exists an R package simest for it, but we used our own implementation. For the MAVE method, we used the R package MAVE; for theory, see Xia (2006). For the EFM estimate (see Cui et al. 2011), we used an \mathrm{R} script, due to Xia Cui and kindly provided to us by her and Rohit Patra. All runs of our simulations can be reproduced by running the R scripts in Groeneboom 2018 . In simulation model 1 , we take \alpha_{0}=(1 / \sqrt{2}, 1 / \sqrt{2})^{T} and X=\left(X_{1}, X_{2}\right)^{T}, where X_{1} and X_{2} are independent Uniform (0,1) variables. The model is now$$
Y=\psi_{0}\left(\alpha_{0}^{T} \boldsymbol{X}\right)+\varepsilon
$$where \psi_{0}(u)=u^{3} and \varepsilon is a standard normal random variable, independent of \boldsymbol{X}. In simulation model 2 , we also take \alpha_{0}=(1 / \sqrt{2}, 1 / \sqrt{2})^{T} and \boldsymbol{X}=\left(X_{1}, X_{2}\right)^{T}, where X_{1} and X_{2} are independent Uniform (0,1) variables. This time, however, the model is (Table 1)$$
Y=\operatorname{Bin}\left(10, \exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right) /\left{1+\exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)\right}\right)
$$see also Table 2 in Balabdaoui et al. (2019a). This means$$
Y=\psi_{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)+\varepsilon $$where$$ \psi{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)=10 \exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right) /\left{1+\exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)\right}, \quad \varepsilon=N{n}-\psi_{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right), $$and$$ N{n}=\operatorname{Bin}\left(10, \frac{\exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right.}{1+\exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)}\right)
$$Note that indeed \mathbb{E}{\varepsilon \mid \boldsymbol{X})=0, but that we do not have independence of \varepsilon and \boldsymbol{X}, as in the previous example. ## 商科代写|计量经济学代写Econometrics代考|Concluding Remarks We replaced the “crossing of zero” estimators in Balabdaoui et al. (2019b) with profile least squares estimators. The asymptotic distribution of the estimators was determined and its behavior illustrated by a simulation study, using the same models as in Balabdaoui et al. (2019a). In the first model, the error is independent of the covariate and homoscedastic and in this case, four of the estimators were efficient. In the other (binomial-logistic) model, the error was dependent on the covariates and not homoscedastic. It was shown that the Simple Score Estimate (SSE) had in fact a smaller asymptotic variance in this model than the other estimators for which the asymptotic variance is known, although the difference is very small and does not really show up in the simulations. There is no uniformly best estimate in our simulation, but the EDR estimate is clearly inferior to the other estimates, including the LSE, in particular for the lower sample sizes. On the other hand, the LSE is inferior to the other estimators except for the EDR. All simulation results can be reproduced by running the R scripts in Groeneboom (2018). ## 商科代写|计量经济学代写Econometrics代考|Mathematical Context We assume to be given a sample \mathscr{D}{n}=\left{\left(X{1}, Y_{1}\right), \ldots,\left(X_{n}, Y_{n}\right)\right} of i.i.d. observations, where each pair \left(X_{i}, Y_{i}\right) takes values in \mathscr{X} \times \mathscr{Y}. Throughout, \mathscr{X} is a Borel subset of \mathbb{R}^{d}, and \mathscr{Y} \subset \mathbb{R} is either a finite set of labels (for classification) or a subset of \mathbb{R} (for regression). The vector space \mathbb{R}^{d} is endowed with the Euclidean norm |\cdot|. Our goal is to construct a predictor F: \mathscr{X} \rightarrow \mathbb{R} that assigns a response to each possible value of an independent random observation distributed as X_{1}. In the context of gradient boosting, this general problem is addressed by considering a class \mathscr{F} of functions f: \mathscr{X} \rightarrow \mathbb{R} (called the weak or base learners) and minimizing some empirical risk functional$$
C_{n}(F)=\frac{1}{n} \sum_{i=1}^{n} \psi\left(F\left(X_{i}\right), Y_{i}\right)
$$over the linear combinations of functions in \mathscr{F}. The function \psi: \mathbb{R} \times \mathscr{Y} \rightarrow \mathbb{R}{+}, called the loss, is convex in its first argument and measures the cost incurred by predicting F\left(X{i}\right) when the answer is Y_{i}. For example, in the least squares regression problem, \psi(x, y)=(y-x)^{2} and$$
C_{n}(F)=\frac{1}{n} \sum_{i=1}^{n}\left(Y_{i}-F\left(X_{i}\right)\right)^{2} .
$$However, many other examples are possible, as we will see below. Let \delta_{z} denote the Dirac measure at z, and let \mu_{n}=(1 / n) \sum_{i=1}^{n} \delta_{\left(X_{i}, Y_{j}\right)} be the empirical measure associated with the sample \mathscr{D}{n}. Clearly,$$ C{n}(F)=\mathbb{E} \psi(F(X), Y),
$$where (X, Y) denotes a random pair with distribution \mu_{n} and the symbol \mathbb{E} denotes the expectation with respect to \mu_{n}. Naturally, the theoretical (i.e., population) version of C_{n} is$$
C(F)=\mathbb{E} \psi\left(F\left(X_{1}\right), Y_{1}\right),
$$where now the expectation is taken with respect to the distribution of \left(X_{1}, Y_{1}\right). It turns out that most of our subsequent developments are independent of the context,whether empirical or theoretical. Therefore, to unify the notation, we let throughout (X, Y) be a generic pair of random variables with distribution \mu_{X, Y}, keeping in mind that \mu_{X, Y} may be the distribution of \left(X_{1}, Y_{1}\right) (theoretical risk), the standard empirical measure \mu_{n} (empirical risk), or any smoothed version of \mu_{n}. ## 计量经济学代考 ## 商科代写|计量经济学代写Econometrics代考|Simulation and Comparisons with Other Estimators 在本节中，我们将 LSE 与简单分数估计 (SSE)、有效分数估计 (ESE)、有效降维 (EDR) 估计、样条估计、MAVE 估计和 EFM 估计进行比较。我们参与了 Balabdaoui 等人的模拟设置。(2019a)，这意味着我们取维度d等于 2 。由于在这种情况下参数属于圆的边界，我们只需要确定一个一维参数。利用这个事实，我们使用参数化一个=(一个1,一个2)=(因⁡(b),罪⁡(b))并确定角度b通过黄金分割搜索 SSE、ESE 和样条估计。对于 EDR，我们使用Rpackage edr：Hristache 等人讨论了该方法。（2001 年）。样条方法在 Kuchibhotla 和 Patra (2020) 中有描述，并且存在R最适合它的包，但我们使用了自己的实现。对于 MAVE 方法，我们使用了 R 包 MAVE；理论见Xia (2006)。对于 EFM 估计（参见 Cui et al. 2011），我们使用了R剧本，感谢夏翠，由她和 Rohit Patra 提供给我们。我们模拟的所有运行都可以通过运行RGroeneboom 中的脚本2018. 在仿真模型 1 中，我们取一个0=(1/2,1/2)吨和X=(X1,X2)吨， 在哪里X1和X2是独立的制服(0,1)变量。模型现在 是=ψ0(一个0吨X)+e 在哪里ψ0(在)=在3和e是标准正态随机变量，独立于X. 在仿真模型 2 中，我们还取一个0=(1/2,1/2)吨和X=(X1,X2)吨， 在哪里X1和X2是独立的制服(0,1)变量。然而，这一次，模型是（表 1） Y=\operatorname{Bin}\left(10, \exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right) /\left{1+\exp \left(\粗体符号{\alpha}{0}^{T} \boldsymbol{X}\right)\right}\right)Y=\operatorname{Bin}\left(10, \exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right) /\left{1+\exp \left(\粗体符号{\alpha}{0}^{T} \boldsymbol{X}\right)\right}\right) 另见 Balabdaoui 等人的表 2。（2019a）。这表示 是=ψ0(一个0吨X)+e在哪里 \psi{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)=10 \exp \left(\boldsymbol{\alpha}{0}^{T} \ boldsymbol{X}\right) /\left{1+\exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)\right}, \quad \varepsilon=N{ n}-\psi_{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right),\psi{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)=10 \exp \left(\boldsymbol{\alpha}{0}^{T} \ boldsymbol{X}\right) /\left{1+\exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)\right}, \quad \varepsilon=N{ n}-\psi_{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right),和 ñn=垃圾桶⁡(10,经验⁡(一个0吨X1+经验⁡(一个0吨X)) 注意确实 \mathbb{E}{\varepsilon \mid \boldsymbol{X})=0,b在吨吨H一个吨在和d○n○吨H一个在和一世nd和p和nd和nC和○F\伐普西隆一个nd\boldsymbol{X}，如上例所示。 ## 商科代写|计量经济学代写Econometrics代考|Concluding Remarks 我们替换了 Balabdaoui 等人的“过零”估计量。（2019b）具有轮廓最小二乘估计器。使用与 Balabdaoui 等人相同的模型，确定了估计量的渐近分布，并通过模拟研究说明了其行为。（2019a）。 在第一个模型中，误差与协变量和同方差无关，在这种情况下，四个估计量是有效的。在另一个（二项式逻辑）模型中，误差取决于协变量而不是同方差。结果表明，与已知渐近方差的其他估计量相比，简单分数估计 (SSE) 实际上在该模型中具有更小的渐近方差，尽管差异非常小并且并未真正显示在模拟中。 在我们的模拟中没有统一的最佳估计，但 EDR 估计明显不如其他估计，包括 LSE，特别是对于较小的样本量。另一方面，LSE 不如 EDR 以外的其他估计量。所有模拟结果都可以通过运行RGroeneboom (2018) 中的脚本。 ## 商科代写|计量经济学代写Econometrics代考|Mathematical Context 我们假设给定一个样本\mathscr{D}{n}=\left{\left(X{1}, Y_{1}\right), \ldots,\left(X_{n}, Y_{n}\right)\right}\mathscr{D}{n}=\left{\left(X{1}, Y_{1}\right), \ldots,\left(X_{n}, Y_{n}\right)\right}独立同分布观察，其中每一对(X一世,是一世)取值X×是. 始终，X是一个 Borel 子集Rd， 和是⊂R是一组有限的标签（用于分类）或R（用于回归）。向量空间Rd被赋予欧几里得范数|⋅|. 我们的目标是构建一个预测器F:X→R将响应分配给独立随机观察的每个可能值，分布为X1. 在梯度提升的背景下，这个一般问题是通过考虑一个类来解决的F功能F:X→R（称为弱学习器或基础学习器）并最小化一些经验风险函数 Cn(F)=1n∑一世=1nψ(F(X一世),是一世) 在函数的线性组合上F. 功能ψ:R×是→R+，称为损失，在其第一个参数中是凸的，并衡量通过预测所产生的成本F(X一世)当答案是是一世. 例如，在最小二乘回归问题中，ψ(X,是)=(是−X)2和 Cn(F)=1n∑一世=1n(是一世−F(X一世))2. 但是，许多其他示例也是可能的，我们将在下面看到。让d和表示狄拉克测度和， 然后让μn=(1/n)∑一世=1nd(X一世,是j)是与样本相关的经验度量Dn. 清楚地， Cn(F)=和ψ(F(X),是), 在哪里(X,是)表示具有分布的随机对μn和符号和表示相对于的期望μn. 自然地，理论（即人口）版本Cn是 C(F)=和ψ(F(X1),是1), 现在的期望是关于分布的(X1,是1). 事实证明，我们随后的大部分发展都独立于背景，无论是经验的还是理论的。因此，为了统一符号，我们让通篇(X,是)是具有分布的通用随机变量对μX,是，请记住μX,是可能是分布(X1,是1)（理论风险），标准经验测量μn（经验风险），或任何平滑版本μn. 统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。 ## 金融工程代写 金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。 ## 非参数统计代写 非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。 ## 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。 术语 广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。 ## 有限元方法代写 有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。 有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。 tatistics-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。 ## 随机分析代写 随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。 ## 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。 ## 商科代写|计量经济学代写Econometrics代考|ECOM20001 如果你也在 怎样代写计量经济学Econometrics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。 计量经济学，对经济关系的统计和数学分析，通常作为经济预测的基础。这种信息有时被政府用来制定经济政策，也被私人企业用来帮助价格、库存和生产方面的决策。 statistics-lab™ 为您的留学生涯保驾护航 在代写计量经济学Econometrics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。我们的专家在代写计量经济学Econometrics代写方面经验极为丰富，各种代写计量经济学Econometrics相关的作业也就用不着说。 我们提供的计量经济学Econometrics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 高等概率论 • 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 ## 商科代写|计量经济学代写Econometrics代考|General Conditions and the Functions ψˆ n,αˆ and ψα We give general conditions that we assume to hold in the remainder of the paper here and give graphical comparisons of the functions \hat{\psi}{n, \alpha} and \psi{\alpha}, where \psi_{\alpha} is defined in Definition 1 . Example 1 As an illustrative example, we take d=2, \psi_{0}(x)=x^{3}, \alpha_{0}=(1 / \sqrt{2}, 1 / \sqrt{2})^{T}, Y_{i}=\psi_{0}\left(\alpha_{0}^{T} X_{i}\right)+\varepsilon_{i}, where the \varepsilon_{i} are i.i.d. standard normal random variables, independent of the \boldsymbol{X}{i}, which are i.i.d. random vectors, consisting of two independent Uniform (0,1) random variables. In this case, the conditional expectation function (5) is a rather complicated function of \alpha which we shall not give here but can be computed by a computer package such as Mathematica or Maple. The loss functions: L^{\mathrm{LSE}}: \alpha{1} \mapsto \mathbb{E}\left{Y-\psi_{\alpha}\left(\alpha^{T} \boldsymbol{X}\right)\right}^{2} \quad and \quad \widehat{L}{n}^{\mathrm{LSE}}: \alpha{1} \mapsto n^{-1} \sum_{i=1}^{n}\left{Y_{i}-\hat{\psi}{n, \alpha}\left(\alpha^{T} \boldsymbol{X}{i}\right)\right}^{2} where the loss function \widehat{L}{n}^{L S E} is for sample sizes n=10,000 and n=100,000, and \alpha=\left(\alpha{1}, \alpha_{2}\right)^{T}. For \alpha_{1} \in[0,1] and \alpha_{2} equal to the positive root \left{1-\alpha_{1}^{2}\right}^{1 / 2}, we get Fig. 1. The function L^{\mathrm{LSE}} has a minimum equal to 1 at \alpha_{1}=1 / \sqrt{2}, and \widehat{L}{n}^{\mathrm{LSE}} has a minimum at a value very close to 1 / \sqrt{2} (furnishing the profile LSE \hat{\alpha}{n} ), which gives a visual evidence for consistency of the profile LSE. In order to show the \sqrt{n}-consistency and asymptotic normality of the estimators in the next sections, we now introduce some conditions, which correspond to those in Balabdaoui et al. (2019b). We note that we do not need conditions on reparameterization. (A1) \boldsymbol{X} has a density w.r.t. Lebesgue measure on its support \mathcal{X}, which is a convex set \mathcal{X} with a nonempty interior, and satisfies \mathcal{X} \subset\left{x \in \mathbb{R}^{d}:|x| \leq R\right} for some R>0. (A2) The function \psi_{0} is bounded on the set \left{u \in \mathbb{R}: u=\alpha_{0}^{T} \boldsymbol{x}, \boldsymbol{x} \in \mathcal{X}\right}. (A3) There exists \delta>0 such that the conditional expectation \tilde{\psi}{\alpha}, defined by (5), is nondecreasing on I{\alpha}=\left{u \in \mathbb{R}: u=\alpha^{T} \boldsymbol{x}, x \in \mathcal{X}\right} and satisfies \bar{\psi}{\alpha}=\psi{\alpha}, so minimizes$$
\left|\mathbb{E}\left{Y-\psi\left(\boldsymbol{\alpha}^{T} \boldsymbol{X}\right)\right} \boldsymbol{X}\right|^{2}
$$over nondecreasing functions \psi, if \left|\boldsymbol{\alpha}-\boldsymbol{\alpha}_{0}\right| \leq \delta. ## 商科代写|计量经济学代写Econometrics代考|The Limit Theory for the SSE In this section, we derive the limit distribution of the SSE introduced above. In our derivation, the function \psi_{\alpha} of Definition 1 plays a crucial role. Below, we will use the following assumptions, additionally to (\mathrm{A} 1)-(\mathrm{A} 6). (A7) There exists a \delta>0 such that for all \alpha \in\left(\mathcal{B}\left(\alpha_{0}, \delta\right) \cap \mathcal{S}{d-1}\right) \backslash\left{\alpha{0}\right}, the random variable$$
\operatorname{cov}\left(\left(\boldsymbol{\alpha}{0}-\boldsymbol{\alpha}\right)^{T} \boldsymbol{X}, \psi{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right) \mid \boldsymbol{\alpha}^{T} \boldsymbol{X}\right) $$is not equal to 0 almost surely. (A8) The matrix$$ \mathbb{E}\left[\psi{0}^{\prime}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right) \operatorname{cov}\left(\boldsymbol{X} \mid \boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)\right]
$$has rank d-1. We start by comparing (3) with the function$$
\alpha \mapsto\left|\mathbb{E}\left{Y-\psi_{\alpha}\left(\alpha^{T} \boldsymbol{X}\right)\right} \boldsymbol{X}\right|^{2}
$$As in Sect. 1, the function \hat{\psi}_{n, \alpha} is just the (isotonic) least squares estimate for fixed \alpha. ## 商科代写|计量经济学代写Econometrics代考|The Limit Theory for ESE and Cubic Spline Estimator The proofs of the consistency and asymptotic normality of the ESE and spline estimator are highly similar to the proofs of these facts for the SSE in the preceding section. The only extra ingredient is the occurrence of the estimate of the derivative of the link function. We only discuss the asymptotic normality. In addition to the assumptions (A1)-(A7), we now assume the following: (A8′) \psi_{\alpha} is twice differentiable on \left.\inf {x \in \mathcal{X}}\left(\alpha^{T} \boldsymbol{x}\right), \sup {x \in \mathcal{X}^{\prime}}\left(\boldsymbol{\alpha}^{T} \boldsymbol{x}\right)\right). (A9) The matrix$$
\mathbb{E}\left[\psi_{0}^{\prime}\left(\alpha_{0}^{T} \boldsymbol{X}\right)^{2} \operatorname{cov}\left(\boldsymbol{X} \mid \alpha_{0}^{T} \boldsymbol{X}\right)\right]
$$has rank d-1. An essential step is again to show that$$
\begin{aligned}
&\int \boldsymbol{x}\left{y-\hat{\psi}{n, \hat{\alpha}{n}}\left(\hat{\boldsymbol{\alpha}}{n}^{T} \boldsymbol{x}\right)\right} \hat{\psi}{n \hat{\boldsymbol{\alpha}}{n}}^{\prime}\left(\hat{\boldsymbol{\alpha}}{n}^{T} \boldsymbol{x}\right) d \mathbb{P}{n}(\boldsymbol{x}, y) \ &=\int\left{\boldsymbol{x}-\mathbb{E}\left(X \mid \hat{\boldsymbol{\alpha}}{n}^{T} \boldsymbol{X}\right)\right}\left{y-\hat{\psi}{n, \hat{\alpha}{n}}\left(\hat{\boldsymbol{\alpha}}{n}^{T} \boldsymbol{x}\right)\right} \hat{\psi}{n \hat{\alpha}{n}}^{\prime}\left(\hat{\alpha}{n}^{T} \boldsymbol{x}\right) d \mathbb{P}{n}(\boldsymbol{x}, y) \ &+o{p}\left(n^{-1 / 2}\right)+o_{p}\left(\hat{\alpha}{n}-\boldsymbol{\alpha}{0}\right)
\end{aligned}
$$For the ESE, this is done by defining the piecewise constant function \bar{\rho}{n, \alpha} for u in the interval between successive jumps \tau{i} and \tau_{i+1} ) of \hat{\psi}{n \alpha} by$$ \bar{\rho}{n, \alpha}(u)= \begin{cases}\mathbb{E}\left[\boldsymbol{X} \mid \alpha^{T} \boldsymbol{X}=\tau_{i}\right] \psi_{\alpha}^{\prime}\left(\tau_{i}\right) & \text { if } \psi_{\alpha}(u)>\hat{\psi}{n \alpha}\left(\tau{i}\right) \text { for all } u \in\left(\tau_{i}, \tau_{i+1}\right) \ \mathbb{E}\left[\boldsymbol{X} \mid \alpha^{T} \boldsymbol{X}=s\right] \psi_{\alpha}^{\prime}(s) & \text { if } \psi_{\alpha}(s)=\hat{\psi}{n \alpha}(s) \text { for some } s \in\left(\tau{i}, \tau_{i+1}\right) \ \mathbb{E}\left[\boldsymbol{X} \mid \alpha^{T} \boldsymbol{X}=\tau_{i+1}\right] \psi_{\alpha}^{\prime}\left(\tau_{i+1}\right) & \text { if } \psi_{\alpha}(u)<\hat{\psi}{n \alpha}\left(\tau{i}\right) \text { for all } u \in\left(\tau_{i}, \tau_{i+1}\right)\end{cases}
$$see Appendix E in the supplement of Balabdaoui et al. (2019b). The remaining part of the proof runs along the same lines as the proof for the SSE. For additional details, see Appendix E in the supplement of Balabdaoui et al. (2019b). The corresponding step in the proof for the spline estimator is given by the following lemma. ## 计量经济学代考 ## 商科代写|计量经济学代写Econometrics代考|General Conditions and the Functions ψˆ n,αˆ and ψα 我们给出了我们假设在本文的其余部分中持有的一般条件，并给出了函数的图形比较 \hat{\psi}, \alpha, \alpha 和 \psi \alpha ，在哪里 \psi_{\alpha} 在 定义中定义 1 . 例 1 作为一个说明性的例子，我们取 d=2, \psi_{0}(x)=x^{3}, \alpha_{0}=(1 / \sqrt{2}, 1 / \sqrt{2})^{T}, Y_{i}=\psi_{0}\left(\alpha_{0}^{T} X_{i}\right)+\varepsilon_{i} ， 其中 \varepsilon_{i} 是独立同分布的标准正态随机变量，独立于 \boldsymbol{X} i ，它们是 iid 随机向量，由两个独立的 Uniform 组成 (0,1) 随机变量。在这种情况下，条件期望函数 (5) 是一个相当复杂的函数 \alpha 我们不会在这里给出，但可以通过诸如 Mathematica 或 Maple 之类的计算机包来计算。损失函数: 和 \mathrm{~ I q u a d ~ I w i d e h a t { { \ { n }} 其中损失函数 \widehat{L} n^{L S E} 适用于样本量 n=10,000 和 n=100,000 ，和 \alpha=\left(\alpha 1, \alpha_{2}\right)^{T}. 为了 \alpha_{1} \in[0,1] 和 \alpha_{2} 等于正根 \mathrm{~ l e f t { 1 – l a l p h a _ { 1 } へ { 2 } \ r i g h t }} \widehat{L} n^{\mathrm{LSE}} 最小值非常接近 1 / \sqrt{2} (提供简介 LSE \left.\hat{\alpha} n\right) ，这为配置文件 LSE 的一致性提供了视觉证据。 为了显示 \sqrt{n}-在下一节中估计量的一致性和渐近正态性，我们现在介绍一些条件，这些条件对应于 Balabdaoui 等 人的条件。(2019b)。我们注意到我们不需要重新参数化的条件。 (A1) \boldsymbol{X} 在其支持上有一个密度 wrt Lebesgue 度量 \mathcal{X} ，这是一个凸集 \mathcal{X} 具有非空的内部，并且满足 \mathrm{~ I m a t h c a l { X } }} (A2) 功能 \psi_{0} 有界在集合上 \eft {u \backslash in \backslash \mathrm{~ m a t h b b b { R } : ~ u =} (A3) 存在 \delta>0 使得条件期望 \tilde{\psi} \alpha ，由 (5) 定义，在 I{\alpha }=\backslash 1 eft \left{u \backslash\right. in \backslash mathbb {R}: u=\backslash a \mid p h a^{\wedge}{T} \backslash boldsymbol {x}, x \backslash \mathrm{~ i n ~} Veft \backslash \backslash mathbb { E } \backslash eft {Y \mathrm{~ – ~ \ p s i V l e f t (} 过非减函数 \psi ，如果 \left|\boldsymbol{\alpha}-\boldsymbol{\alpha}_{0}\right| \leq \delta. ## 商科代写|计量经济学代写Econometrics代考|The Limit Theory for the SSE 在本节中，我们推导出上面介绍的 SSE 的极限分布。在我们的推导中，函数 \psi_{\alpha} 定义 1 起着至关重要的作用。下 面，我们将使用以下假设，此外 (\mathrm{A} 1)-(\mathrm{A} 6). (A7) 存在一个 \delta>0 这样对于所有人 \mathrm{~ \ a l p h a ~ \ i n \ l e f t ( \ m a t h c a l { B }} 变量$$
\operatorname{cov}\left((\boldsymbol{\alpha} 0-\boldsymbol{\alpha})^{T} \boldsymbol{X}, \psi 0\left(\boldsymbol{\alpha} 0^{T} \boldsymbol{X}\right) \mid \boldsymbol{\alpha}^{T} \boldsymbol{X}\right)
$$几乎肯定不等于 0 。 (A8) 矩阵$$
\mathbb{E}\left[\psi 0^{\prime}\left(\boldsymbol{\alpha} 0^{T} \boldsymbol{X}\right) \operatorname{cov}\left(\boldsymbol{X} \mid \boldsymbol{\alpha} 0^{T} \boldsymbol{X}\right)\right]
$$有等级 d-1. 我们首先将 (3) 与函数进行比较 \alpha \mapsto\left } \backslash \backslash \text { mathbb } { E } \backslash l e f t { Y \mathrm { ~ – 就像在教派中一样。1、功能 \hat{\psi}_{n, \alpha} 只是固定的 (等渗的) 最小二乘估计 \alpha. ## 商科代写|计量经济学代写Econometrics代考|The Limit Theory for ESE and Cubic Spline Estimator ESE 和样条估计量的一致性和渐近正态性的证明与上一节中 SSE 的这些事实的证明非常相似。唯一的额外因素是链 接函数导数估计的出现。我们只讨论渐近正态性。 除了假设（A1 ) – (A7)，我们现在假设以下: (A8′) \psi_{\alpha} 是两次可微的 \left.\inf x \in \mathcal{X}\left(\alpha^{T} \boldsymbol{x}\right), \sup x \in \mathcal{X}^{\prime}\left(\boldsymbol{\alpha}^{T} \boldsymbol{x}\right)\right). (A9) 矩阵$$
\mathbb{E}\left[\psi_{0}^{\prime}\left(\alpha_{0}^{T} \boldsymbol{X}\right)^{2} \operatorname{cov}\left(\boldsymbol{X} \mid \alpha_{0}^{T} \boldsymbol{X}\right)\right]


\begin } { \text { 对齐 } } \text { \& Int } \backslash \text { boldsymbol } { x } \backslash l e f t { y \mathrm { ~ – ~

## 有限元方法代写

tatistics-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。

## 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。

## 商科代写|商业建模代写Business Modeling代考|INFS6016

statistics-lab™ 为您的留学生涯保驾护航 在代写商业建模Business Modeling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。我们的专家在代写商业建模Business Modeling代写方面经验极为丰富，各种代写商业建模Business Modeling相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• 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

## 商科代写|商业建模代写Business Modeling代考|Process Flow

When we look at the work of Shigeo Shingo about improvement of production processes, he is not talking about processes as such, but rather at process delays. Essentially, he is discussing lossless transitions between (sub)processes and reduction of avoidable waste in transformation (sub)processes [6]. Any storage that is not required for stabilisation of the product is considered a process delay, and as such a loss to be avoided. However, when the period between order and delivery is shorter than the actual time it takes to manufacture a product, stocks are necessary. Therefore, reduction of process delay is key to Shingo’s thinking. Faster production throughput implies less need for stocks, and shifts production from push to pull.

Process improvement is fundamentally about time and timing. Underutilisation of production capacity is allowed when it reduces significantly throughput time. As an example, imagine a production company where the packaging is the bottleneck. The company has to find a balance between order lead time, customer service levels, idle time of expensive packaging equipment, and scrapped stock waiting for orders that did not materialise. Considerations of production cost would argue against investments in equipment, market considerations would argue against higher lead times. Taiichi Ohno writes “In production, ‘waste’ refers to all elements of production that only increase cost without adding value – for example, excess people, inventory, and equipment” [7]. The company will have to balance excess equipment against excess stocks. “Idle equipment” cannot always be equated to “excess equipment”.

To summarise, this kind of process thinking is primarily about pull, flow and avoidance of delays. This requires balancing on both the design level (production capacities) and the operational level (mechanisms for mutual adjustment/modification of production capacities). Processes can be recognised on different aggregation levels. They can be continuous or discrete. To realise flow through processes mechanisms must be in place that prevent unwanted intermediate stocks and unnecessary waiting between (sub)processes.

The relation of a business process to preceding and subsequent processes is another thing. The classic waterfall approach of IT projects is a prototypical example where each subsequent process is triggered by its preceding process and the chain of processes is carried out linearly, without going back to previous processes, until the end result. A second kind of process structure is linear with feedback, either directly feeding information back to a preceding process, or indirectly via some monitoring process. This process structure is found in conventional production companies. A third kind of process structure is with mutual adjustment between preceding and subsequent processes. Here a kind of reciprocity is to be found between preceding and subsequent processes, and this process structure is more likely to be found in production organisations that are based on the lean ideas.

## 商科代写|商业建模代写Business Modeling代考|Coping with Variability

In order to create constant outputs that are useful for customers or internal subsequent processes, business processes must be able to absorb variability. Irregularities in inputs or in the processing that are not absorbed will be passed on as irregularities in outputs.

Often, there will be a trade-off between extra costs caused by eliminating variability in the processes (creating extra consumption of resources. extra waste, and/or late delivery) and the extra costs of not fulfilling specifications and expectations for customers or for subsequent processes. Dealing with such trade-offs might be subject to coordination processes within the company or between the company and its customers.
In the design and execution of business processes there are different dimensions of variability, and different ways for coping with variability. One dimension is quality and deals with specifications and tolerances. Elimination of output variability can be achieved by elimination of variability of input in combination with standardisation of processes (Mintzberg: standardisation of work) [8]. A second way of elimination of output variability is to allow variability of input and have processes in place that eliminate variability in the processes (Mintzberg: standardisation of output). The third option is to allow variability at the output of the process, and then the question is how much the customer or the next internal process can and will tolerate.

Another dimension of variability is quantity and timing. This dimension is about getting the right amount of output at the right time available out of the process, and this requires the right amounts of resources at the right time available for consumption in the process. Some variability will be absorbed in the process. Variability in quantity and time between processes must be resolved by mutual adjustments of the processes, or by rescheduling. Major readjustments will be made dependent on a broad range of competing values. Will a delivery be on time but incomplete, or late and complete? Will an internal process be on time but generate extra costs, or late without extra production costs? This kind of decision making might also depend on the creativity of experienced people. Sometimes people can find smart ways to lessen the negative effects of product or production variability, by balancing requirements and possibilities of efficiency, specifications, timing, and allowable tolerances. Decision making in this kind of adjustment processes requires that a broad range of experience and competence is represented, because (1) heterogeneous values must be weighed against each other and (2) detailed knowledge about processes is needed to evaluate what is really possible in the given situation. And, where the output for customers is affected, both the specific agreement with the customer and the general conventions are important factors in balancing obligations and costs.

## 商科代写|商业建模代写Business Modeling代考|Machine Metaphor

Gareth Morgan wrote about the mechanical view on organisations “When we talk about an organisation, we usually have in mind a state of orderly relations between clearly defined parts that have some determinate order. Although the image may not be explicit, we are talking about a set of mechanical relations. We talk about organisations as if they were machines, and as a consequence we tend to expect them to operate as machines: in a routinized, efficient, reliable, and predictable way” [9]. Peter Senge wrote about the machine metaphor something similar: “A machine exists for a purpose conceived of by its builders” and “To be effective, a machine must be controllable by its operators. This, of course, is the raison d’être of management – to control the enterprise” [10]. Such a view on organisations is reflected in the usage of the concept of enterprise engineering, which suggests that a company can be engineered like a machine. The Complete Business Process Handbook defines a business process “as a collection of tasks and activities (business operations and actions) consisting of employees, materials, machines, systems and methods that are being structured in such a way as to design, create, and deliver a product or service to the customer” [11] In the formal BPMN specification of the OMG a business process is defined as “A defined set of business activities that represent the steps required to achieve a business objective. It includes the flow and use of information and resources.” [12] These definitions match pretty good with the OED entry for a machine “An apparatus for applying mechanical power, consisting of a number of interrelated parts, each having a definite function” [1], apart from the application of mechanical power.

Of course, Morgan has offered not only the machine metaphor, but also the metaphors for the organisation as an organism, as a brain, as a culture, as political system, as psychic prison, as flux and transformation, and as domination. Each metaphor helps to see certain aspects of an organisation by comparing typical organisational features with features of the concept of the machine, organism, brain, et cetera. In this sense each metaphor is “true” in the sense that the organisation can be considered to have similar features as a machine. At the same time, the concepts brought together in the metaphor differ in many other respects. Morgan has described this paradox of the metaphor as the phenomenon that the statement “A is $\mathrm{B}$ ” can be both very useful and patently false at the same time. Taken metaphorically, the statement “the organisation is a machine” or “the organisation is an organism” can generate insights in the workings of an organisation as a consequence of the similarities between machine and organisation or between an organism and an organisation.

## 有限元方法代写

tatistics-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。

## 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。