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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写Economics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Economics代写方面经验极为丰富，各种代写Economics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|回归分析作业代写Regression Analysis代考|Estimating Regression Model Parameters

So, LOESS is good but not necessarily best. Sometimes linear models are good even though they are almost always wrong. How can you know which estimates to use?

Besides simulation, another guiding principle we will use throughout this book is likelihood. Methods based on likelihood are usually excellent. While not infallible, they can be considered as a “gold standard” of statistical methods: If your data come from particular models $p(y \mid x)$, and if you analyze your data using maximum likelihood that assumes those same particular models, then your analysis will be nearly ideal.

Least squares estimation, the most common method for analyzing regression data, is itself motivated by likelihood, since the least squares estimates are in fact the maximum likelihood estimates that you get when you assume $p(y \mid x)$ is a normal distribution. This fact can be viewed as a lucky coincidence: If the normal distribution did not have a squared term in its exponent, then you would not use least squares. Instead, you would use least absolute deviations, or some other method, as the default for regression analysis.

In addition, likelihood-based methods are an essential first step toward Bayesian methods, which are rapidly becoming an essential statistical tool for all scientists. Finally, standard methods for regression with non-normal distributions, such as logistic regression and Poisson regression use likelihood-based analyses by default, so you need to understand likelihood in order to read the computer output.

We begin this chapter by reviewing likelihood-based methods, with special attention to their use in regression.

## 统计代写|回归分析作业代写Regression Analysis代考|Maximum Likelihood with Non-normal Distributions

The ordinary least squares (OLS) estimates are maximum likelihood estimates from the classical, normally distributed model. But just as linearity is never precisely true, normality is never precisely true either. There are always asymmetries, levels of discreteness, levels of outlier potential, and boundedness characteristics that make all real data-generating processes non-normal. Can you still use OLS, then? The answer is yes-as with any statistical procedure based on the assumption of normality, you can still use it with non-normal distributions. The procedure will be reasonably good if the distributions that produced the data are reasonably close to normal distributions. But, if the distributions are far from normal, other methods may be better.

An interesting alternative to the normal distribution is the Laplace distribution, for which
$$p(y)=\frac{1}{\sqrt{2} \sigma} \exp \left[-\sqrt{2} \frac{|y-\mu|}{\sigma}\right]$$
The mathematical form of the Laplace distribution looks similar to that of the normal distribution, but since the values in the exponent are absolute deviations from the mean rather than squared deviations, the Laplace distribution allows much higher probability that an observation can be far from the mean. In other words, the Laplace distribution allows a higher probability of an extreme observation, commonly called an outlier. The excess kurtosis of the Laplace distribution is 3 (that of the normal distribution is 0 ), which also implies that the Laplace distribution is more outlier-prone than the normal distribution.

Figure $2.2$ compares the normal distribution with $\mu=0, \sigma=1$ with the corresponding Laplace distribution. Notice that the Laplace distribution extends farther into the tails, despite the fact both distributions have the same standard deviation.

# 回归分析代写

## 统计代写|回归分析作业代写Regression Analysis代考|Maximum Likelihood with Non-normal Distributions

$$p(y)=\frac{1}{\sqrt{2} \sigma} \exp \left[-\sqrt{2} \frac{|y-\mu|}{\sigma}\right]$$

## 有限元方法代写

assignmentutor™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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师