### 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|OLET5610

statistics-lab™ 为您的留学生涯保驾护航 在代写多元统计分析Multivariate Statistical 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。我们的专家在代写多元统计分析Multivariate Statistical Analysis代写方面经验极为丰富，各种代写多元统计分析Multivariate Statistical Analysis相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|多元统计分析代写Multivariate Statistical Analysis代考|Comparison of Batches

Multivariate statistical analysis is concerned with analysing and understanding data in high dimensions. We suppose that we are given a set $\left{x_{i}\right}_{i=1}^{n}$ of $n$ observations of a variable vector $X$ in $\mathbb{R}^{p}$. That is, we suppose that each observation $x_{i}$ has $p$ dimensions:
$$x_{i}=\left(x_{i 1}, x_{i 2}, \ldots, x_{i p}\right)$$
and that it is an observed value of a variable vector $X \in \mathbb{R}^{p}$. Therefore, $X$ is composed of $p$ random variables:
$$X=\left(X_{1}, X_{2}, \ldots, X_{p}\right)$$
where $X_{j}$, for $j=1, \ldots, p$, is a one-dimensional random variable. How do we begin to analyse this kind of data? Before we investigate questions on what inferences we can reach from the data, we should think about how to look at the data. This involves descriptive techniques. Questions that we could answer by descriptive techniques are:

• Are there components of $X$ that are more spread out than others?
• Are there some elements of $X$ that indicate sub-groups of the data?
• Are there outliers in the components of $X$ ?
• How “normal” is the distribution of the data?
• Are there “low-dimensional” linear combinations of $X$ that show “non-normal” behaviour?

One difficulty of descriptive methods for high-dimensional data is the human perceptional system. Point clouds in two dimensions are easy to understand and to interpret. With modern interactive computing techniques we have the possibility to see real time $3 \mathrm{D}$ rotations and thus to perceive also three-dimensional data. A “sliding technique” as described in Härdle and Scott (1992) may give insight into four-dimensional structures by presenting dynamic 3D density contours as the fourth variable is changed over its range.

## 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Histograms

Histograms are density estimates. A density estimate gives a good impression of the distribution of the data. In contrast to boxplots, density estimates show possible multimodality of the data. The idea is to locally represent the data density by counting the number of observations in a sequence of consecutive intervals (bins) with origin $x_{0}$. Let $B_{j}\left(x_{0}, h\right)$ denote the bin of length $h$ which is the element of a bin grid starting at $x_{0}$ :
$$B_{j}\left(x_{0}, h\right)=\left[x_{0}+(j-1) h, x_{0}+j h\right), \quad j \in \mathbb{Z},$$
where [., . ) denotes a left closed and right open interval. If $\left{x_{i}\right}_{i=1}^{n}$ is an i.i.d. sample with density $f$, the histogram is defined as follows:
$$\hat{f}{h}(x)=n^{-1} h^{-1} \sum{j \in \mathbb{Z}} \sum_{i=1}^{n} \boldsymbol{I}\left{x_{i} \in B_{j}\left(x_{0}, h\right)\right} \mathbf{I}\left{x \in B_{j}\left(x_{0}, h\right)\right}$$
In sum (1.7) the first indicator function $I\left{x_{i} \in B_{j}\left(x_{0}, h\right)\right}$ (see Symbols and Notation in Chap. 21) counts the number of observations falling into bin $B_{j}\left(x_{0}, h\right)$. The second indicator function is responsible for “localising” the counts around $x$. The parameter $h$ is a smoothing or localising parameter and controls the width of the histogram bins. An $h$ that is too large leads to very big blocks and thus to a very unstructured histogram. On the other hand, an $h$ that is too small gives a very variable estimate with many unimportant peaks.

The effect of $h$ is given in detail in Fig. 1.6. It contains the histogram (upper left) for the diagonal of the counterfeit bank notes for $x_{0}=137.8$ (the minimum of these observations) and $h=0.1$. Increasing $h$ to $h=0.2$ and using the same origin, $x_{0}=137.8$, results in the histogram shown in the lower left of the figure. This density histogram is somewhat smoother due to the larger $h$. The binwidth is next set to $h=0.3$ (upper right). From this histogram, one has the impression that the distribution of the diagonal is bimodal with peaks at about $138.5$ and 139.9.

## 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Comparison of Batches

$$x_{i}=\left(x_{i 1}, x_{i 2}, \ldots, x_{i p}\right)$$

$$X=\left(X_{1}, X_{2}, \ldots, X_{p}\right)$$

• 有没有成分 $X$ 比其他人更分散?
• 有没有一些元素 $X$ 表示数据的子组?
• 组件中是否存在异常值 $X$ ?
• 数据的分布有多”正常”?
• 是否存在”低维”线性组合 $X$ 显示”非正常”行为?
高维数据描述方法的一个难点是人类感知系统。二维点云易于理解和解释。借助现代交互式计算技术，我们可 以实时查看3D旋转，因此也可以感知三维数据。Härdle 和 Scott (1992) 中描述的“滑动技术”可以通过在第四个 变量在其范围内发生变化时呈现动态 3D 密度轮廓来深入了解四维结构。

## 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Histograms

$$B_{j}\left(x_{0}, h\right)=\left[x_{0}+(j-1) h, x_{0}+j h\right), \quad j \in \mathbb{Z},$$

## 有限元方法代写

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## 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。