## 统计代写|统计推断代写Statistical inference代考|STAT3013

2023年3月23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|统计推断代写Statistical inference代考|The Concept of a Statistical Model: A Preliminary View

The concept of a random variable $X($.$) played a crucial role in transforming the original$ $(S, \Im, \mathbb{P}(.))^n$ into a statistical model $\mathcal{M}\theta(\mathbf{x})$ defined on the real line: $$(S, \Im, \mathbb{P}(.))^n \quad \stackrel{X(.)}{\longrightarrow} \quad \mathcal{M}\theta(\mathbf{x})=\left{f(\mathbf{x} ; \boldsymbol{\theta}), \boldsymbol{\theta} \in \Theta \subset \mathbb{R}^m\right}, \mathbf{x} \in \mathbb{R}_X^n, m<n$$

where $f(\mathbf{x} ; \boldsymbol{\theta}), \mathbf{x} \in \mathbb{R}_X^n$ denotes the (joint) distribution of the sample $\mathbf{X}:=\left(X_1, \ldots, X_n\right)$, and $\Theta$ the parameter space. Two of the most widely used simple statistical models are given in Tables 4.9 and 4.10 .

In practice, empirical modeling commences from the “set of all possible probability models,” say $\mathcal{P}(\mathbf{x})$, that could have given rise to the particular data $\mathbf{x}_0:=\left(x_1, x_2, \ldots, x_n\right)$. The set $\mathcal{P}(\mathbf{x})$ is chosen based on information relating to the form and structure of the data. That is, the modeler narrows this set down to a subset $\mathcal{P}_0 \subset \mathcal{P}$ of admissible probability models by choosing $f(\mathbf{x} ; \boldsymbol{\theta})$ and $\mathbb{R}_X^*$ felicitously.

The concept of a simple probability model was illustrated in Chapter 3 with a number of density plots for different values of $\boldsymbol{\theta}$. As we will see in Chapter 5 , the choice of $f(\mathbf{x} ; \boldsymbol{\theta})$ does not have to be a hit-or-miss affair; its selection can be expedited by a number of data plots that help to make educated guesses at the appropriateness of different families of densities. The support of the density also plays an important role in the specification, because the range of values of the observed data is a crucial dimension of modeling which is often neglected. In the case where the observed data refer to a data series measured in terms of proportions (i.e. the values taken by the data lie in the interval $[0,1]$ ), postulating a family of densities with support $(-\infty, \infty)$ is often inappropriate. Using the beta distribution might be more appropriate.

Example 4.51 In the case of the exam scores data in Table 1.6, there are good reasons to believe that the range of values (support) of the data suggests that the beta probability model might be a more appropriate choice.

## 统计代写|统计推断代写Statistical inference代考|Statistical Identification of Parameters

It must be emphasized at the outset that for modeling purposes the parameters $\theta \in \Theta$ must be associated with a unique probability distribution $f(\mathbf{x} ; \boldsymbol{\theta})$, otherwise our choice of a good estimator of $\theta$, and thus our choice of stochastic mechanism as given in (4.54), is meaningless. In other words, it is imperative that for different values of $\theta$ in $\Theta$ there correspond different distributions:
Identification for all $\boldsymbol{\theta}1 \neq \boldsymbol{\theta}_2$ where $\boldsymbol{\theta}_1 \in \Theta, \boldsymbol{\theta}_2 \in \Theta, f\left(\mathbf{x} ; \boldsymbol{\theta}_1\right) \neq f\left(\mathbf{x} ; \boldsymbol{\theta}_2\right), \mathbf{x} \in \mathbb{R}_X^n$. That is, a parameter vector $\theta$ is said to be identified when it is uniquely defined by the distribution of the sample $f(\mathbf{x} ; \boldsymbol{\theta}), \mathbf{x} \in \mathbb{R}_X^n$. This uniqueness is defined up to a one-to-one mapping. When specifying the statistical model (4.54), the modeler can choose a number of equivalent parameterizations using a one-to-one mapping. In particular, an equivalent parameterization of $(4.54)$ is $$\mathcal{M}\psi(\mathbf{x})=\left{f(\mathbf{x} ; \psi), \psi \in \Psi, \mathbf{x} \in \mathbb{R}_X^n\right}$$
only when there exists a one-to-one mapping $\psi=\mathbf{g}(\theta): \mathbf{g}():. \Theta \rightarrow \Psi$.

# 统计推断代考

## 统计代写|统计推断代写Statistical inference代考|The Concept of a Statistical Model: A Preliminary View

)playedacrucialroleintrans formingtheoriginal $(S, \mathfrak{I}, \mathbb{P}(.))^n$ 进入统计模型 $\mathcal{M} \theta(\mathbf{x})$ 在实线上定义:
$\left.(\mathrm{S}, \backslash \mathrm{Im}, \backslash m a t h b b{P}(.))^{\wedge} n \backslash q u a d \backslash s t a c k r e \mid{X()}.\right} \backslash$ longrightarr

$\mathbf{x}_0:=\left(x_1, x_2, \ldots, x_n\right)$. 套装 $\mathcal{P}(\mathbf{x})$ 基于与数据的形式 和结构相关的信息来选择。也就是说，建模者将这个集合 缩小到一个子集 $\mathcal{P}_0 \subset \mathcal{P}$ 通过选择可接受的概率模型 $f(\mathbf{x} ; \boldsymbol{\theta})$ 和 $\mathbb{R}_X^*$ 恰到好处地

## 统计代写|统计推断代写Statistical inference代考|Statistical Identification of Parameters

Imathca ${\mathrm{M}} \backslash$ psi $(\backslash m a t h b f{x})=\backslash \operatorname{lft}{f(\backslash m a t h b f{x} ; \backslash p s i), \backslash p$

## 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。