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• 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|时间序列分析代写Time-Series Analysis代考|Orthogonal rotation

Let $\mathbf{F}{t}^{}$ be the rotated factor and $\mathbf{L}^{}=\left[\hat{\ell}{i, j}^{}\right]$ be the rotated matrix of factor loadings. One of the most widely used orthogonal rotation methods is the varimax proposed by Kaiser (1958), which finds an orthogonal transformation to maximize the sum of the variances of the squared loadings: $$V=\frac{1}{m} \sum_{j=1}^{k}\left[\sum_{i=1}^{m}{\tilde{\ell_{i}}}{i}^{}-\frac{1}{m}\left(\sum{i=1}^{m} \tilde{e}{i, j}^{{ }^{2}}\right)^{2}\right]$$ where $$\widetilde{\ell}{i, j}^{}=\frac{\hat{\ell}{i, j}^{}}{\hat{c}{i}},$$
are the rotated coefticients scaled by the square root of communalities. The varimax will be achieved if any given variable has a high loading on a single factor but nearly zero loadings on the remaining factors or any given factor is formed by only a few variables with very high loadings and the remaining variables have nearly zero loadings on this factor. This is a widely used method for orthogonal rotation with all factors remaining uncorrelated. After the orthogonal transformation is determined, we will multiply the loadings $\tilde{\ell}{i, j}^{*}$ by $\hat{c}{i}$ so that the original communalities are preserved.

## 统计代写|时间序列分析代写Time-Series Analysis代考|Oblique rotation

The orthogonal rotation methods like varimax assume that the factors in the analysis are independent. On the other hand, some researchers believe that the purpose of factor rotations is to achieve a simple structure with a new set of factor loadings so that the resulting common factors have simpler and nicer interpretations, and hence one should relax the independence assumption for the factors. The resulting method is often known as oblique rotation. Just like orthogonal rotations, there are many different forms of oblique rotation, see Carroll $(1953,1957)$, and Jennrich and Sampson (1966).

Although we introduce the rotation concept here, they are used for principal components analysis (PCA) too. There are many factor rotations available and they are implemented in statistical software like EViews, MATLAB, MINITAB, R, SAS, and SPSS. We will not spend more time on the discussion of various factor rotations. Instead, we would like to point out that the rationale of factor rotations is to simplify the factor structure with easier interpretation, and Thurstonc (1947) suggested the following critcria:

1. Each variable should produce at least one zero loading on some factor.
2. Each factor should have at least as many nearly zero loadings as there are factors.
4. Each pair of factors should have a large proportion of zero loadings on both factors.

# 时间序列分析代考

## 统计代写|时间序列分析代写Time-Series Analysis代考|Orthogonal rotation

$$\tilde{\ell} i, j=\frac{\hat{\ell} i, j}{\hat{c} i},$$

## 统计代写|时间序列分析代写Time-Series Analysis代考|Oblique rotation

1. 每个变量都应在某个因素上产生至少一个零负载。
2. 每个因子至少应具有与因子一样多的接近零载荷。
3. 每对因子都应具有变量，其中一个具有显着负载，而另一个具有接近于零的负载。
4. 每对因子都应该在两个因子上都具有很大比例的零载荷。

## 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。

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