## 统计代写|回归分析作业代写Regression Analysis代考|STAT5110

2022年10月17日

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

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.

## 统计代写|回归分析作业代写Regression Analysis代考|The Classical Model and Its Consequences

The classical regression model assumes normality, independence, constant variance, and linearity of the conditional mean function, and is (once again) stated as follows:
$$Y_i \mid X_i=x_i \quad \sim_{\text {independent }} \mathrm{N}\left(\beta_0+\beta_1 x_i, \sigma^2\right) \text {, for } i=1,2, \ldots, n .$$
Whether you like it or not, this model is also what your computer assumes when you ask it to analyze your data via standard regression methods. The parameter estimates you get from the computer are best under this model, and the inferences ( $p$-values and confidence intervals) are exactly correct under this model. If the assumptions of the model are not true, then the estimates are not best, and the inferences are incorrect. You might think we are saying that assumptions must be true in order to use statistical methods that make such assumptions, but we are not. As we noted in Chapter 1, it is not necessarily a problem that any or all of the assumptions of the model are wrong, depending on how badly violated is the assumption. And the easiest way to understand whether an assumption is violated “too badly” is to use simulation.

We have found that students in statistics classes often resist learning simulation. After all, the data that researchers use is usually real, and not simulated, so the students wonder, what is the point of using simulation? Here are some answers:

• Simulation shows you, clearly and concretely, how to interpret the regression analysis of your real (not simulated) data.
• Simulation helps you to understand how a regression model can be useful even when the model is wrong.
• Simulation models help you to understand the meaning of the regression model parameters.
• Simulation models help you to understand the meaning of the regression model assumptions.
• Simulation models help you to understand the meaning of a “research hypothesis.”
• Simulation helps you to understand how to interpret your data in the presence of chance effects.
• Simulation helps you to understand all the commonly misunderstood concepts in statistics, like “unbiasedness,” “standard error,” “p-value,” and “confidence interval.”
• Simulation methods are commonly used in the analysis of real data; examples include the bootstrap and Markov Chain Monte Carlo.

An alternative to using simulation is to use advanced mathematics, typically involving multidimensional calculus. But this is much, much harder than simulation.

# 回归分析代写

## 统计代写|回归分析作业代写回归分析代考|非正态分布的极大似然给出非ols估计

$$p(y)=\frac{1}{\sqrt{2} \sigma} \exp \left[-\sqrt{2} \frac{|y-\mu|}{\sigma}\right]$$拉普拉斯分布的数学形式看起来类似于正态分布，但由于指数中的值是对平均值的绝对偏差，而不是方差的平方偏差，因此拉普拉斯分布允许观测值远离平均值的概率更高。换句话说，拉普拉斯分布允许出现一个极端观测值(通常称为离群值)的更高概率。拉普拉斯分布的超额峰度为3(正态分布的超额峰度为0)，这也意味着拉普拉斯分布比正态分布更容易出现异常值

## 统计代写|回归分析作业代写回归分析代考|经典模型及其后果

• 模拟向您清楚而具体地展示如何解释真实(非模拟)数据的回归分析。
• 通过模拟可以帮助您理解一个回归模型是如何在模型错误的情况下发挥作用的。
• 模拟模型可以帮助您理解回归模型参数的含义。
• 模拟模型帮助您理解回归模型假设的意义。
• 模拟模型帮助您理解“研究假设”的含义。
• 模拟帮助您理解在存在机会效应的情况下如何解释数据。模拟帮助你理解统计中所有常被误解的概念，如“无偏”、“标准误差”、“p值”和“置信区间”。模拟方法通常用于对真实数据的分析;例子包括bootstrap和马尔可夫链蒙特卡洛。

## 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。