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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|广义线性模型代写generalized linear model代考|MODELS THAT ADMIT RESTRICTIONS

We begin our model discussion with an example. Consider a group of $b$ tr ex= perimental units. Separate the units into $b$ homogeneous groups with $\operatorname{tr}$ units per group. In each group (or random block) randomly assign $r$ replicate units to each of the $t$ fixed treatment levels. The observed data for this two-way mixed experiment with replication are given in Figure 4.1.1.

A model for this experiment is
$$Y_{i j k}=\mu_j+B_i+B T_{i j}+R(B T){(i j) k}$$ for $i=1, \ldots, b, j=1, \ldots, t$, and $k=1, \ldots, r$ where $Y{i j k}$ is a random variable representing the $k^{\text {th }}$ replicate value in the $i j^{\text {th }}$ block treatment combination; $\mu_j$ is a constant representing the mean effect of the $j^{\text {th }}$ fixed treatment; $B_i$ is a random variable representing the effect of the $i^{\text {th }}$ random block; $B T_{i j}$ is a random variable representing the interaction of the $i^{\text {th }}$ random block and the $j^{\text {th }}$ fixed treatment; and $R(B T)_{(i j) k}$ is a random variable representing the effect of the $k^{\text {th }}$ replicate unit nested in the $i j^{\text {th }}$ block treatment combination.

We now attempt to develop a reasonable set of distributional assumptions for the random variables $B_i, B T_{i j}$, and $R(B T)_{(i j) k}$. Start by considering the $b t r$ observed data points in the experiment as a collection of values sampled from an entire population of possible values. The population for this experiment can be viewed as a rectangular grid with an infinite number of columns, exactly $t$ rows, and an infinite number of possible observed values in each row-column combination (see Figure 4.1.2). The infinite number of columns represents the infinite number of blocks in the population. Each block (or column) contains exactly $t$ rows, one for each level of the fixed treatments. Then the population contains an infinite number of replicate observed values nested in each block treatment combination. The btr observed data points for the experiment are then sampled from this infinite population of values in the following way. Exactly $b$ blocks are selected at random from the infinite number of blocks in the population. For each block selected, all $t$ of the treatment rows are then included in the sample. Finally, within the selected block treatment combinations, $r$ replicate observations are randomly sampled from the infinite number of nested population replicates.

## 统计代写|广义线性模型代写generalized linear model代考|MODELS THAT DO NOT ADMIT RESTRICTIONS

Consider the same experiment discussed in Section 4.1. Use a model with the same variables
$$Y_{i j k}=\mu_j+B_i+B T_{i j}+R(B T)_{(i j) k}$$
where all variables and constants represent the same effects as previously stated. In this model formulation, the population has an infinite number of random blocks. For each block, an infinite number of replicates of each of the $t$ treatment levels exists. Each of these treatment level replicates contains an infinite number of experimental units (see Figure 4.2.1).

The btr observed values for the experiment are sampled from the population by first choosing $b$ blocks at random from the infinite number of blocks in the population. For each selected block, one replicate of each of the $t$ treatment levels is selected. Finally, within the selected block treatment combinations, $r$ replicate observations are randomly sampled. Since the blocks are randomly selected from one infinite population of blocks, assume the random variables $B_i$ are independent, identically distributed. With a normality and zero expectation assumption, let the $b$ block random variables $B_i \sim$ iid $\mathrm{N}1\left(0, \sigma_B^2\right)$. Since the $t$ observed treatment levels are randomly chosen from an infinite population of treatment replicates, an infinite number of possible values are available for the random variables $B T{i j}$. Assume that the average influence of $B T_{i j}$ is zero for each block. But now $\mathrm{E}\left[B T_{i j}\right]=0$ does not imply $\sum_{j=1}^t B T_{i j}=0$ for each $i$ since the variables $B T_{i j}$ have an infinite population. Therefore, a zero expectation does not imply dependence. With a normality assumption, let the $b t$ random variables $B \bar{T}{i j} \sim i i d \mathrm{~N}_1\left(\overline{0}, \sigma{B T}^2\right)$. Finally,within each block treatment combination, the nested replicates are assumed to be sampled from an infinite population. With a normality and zèo expectation assumption, let the btr random variables $R(B T){(i j) k} \sim$ iid $\mathrm{N}_1\left(0, \sigma{R(B T)}^2\right)$. Furthermore, assume that random variables $B_i$, the random variables $B T_{i j}$, and the random variables $R(B T)_{(i j) k}$ are mutually independent. Hence, in models that do not admit restrictions, all variables on the right side of the model are assumed to be independent. Kempthorne (1952) called such models infinite models, because it is assumed that all of the random components are sampled from infinite populations.

# 广义线性模型代考

## 统计代写|广义线性模型代写generalized linear model代考|MODELS THAT ADMIT RESTRICTIONS

$$Y_{i j k}=\mu_j+B_i+B T_{i j}+R(B T)(i j) k$$

## 统计代写|广义线性模型代写generalized linear model代考|MODELS THAT DO NOT ADMIT RESTRICTIONS

$$Y_{i j k}=\mu_j+B_i+B T_{i j}+R(B T){(i j) k}$$ 其中所有变量和常数都表示与前面所述相同的效果。在此模型公式中，总体具有无限数量的随机块。对于每个块，每个块的无限次重复 $t$ 治疗水平存在。这些处理水 平重复中的每一个都包含无限数量的实验单元 (参见图 4.2.1)。 实验的 btr 观察值是通过首先选择从总体中抽样的 $b$ 从种群中无限数量的块中随机抽取块。对于每个选定的块，每个块的一个重复 $t$ 选择治疗水平。最后，在选定的 块处理组合内， $r$ 重复观察是随机抽样的。由于这些块是从无限的块中随机选择的，因此假设随机变量 $B_i$ 是独立的，同分布的。在正态性和零期望假设下，让 $b$ 块随 机变量 $B_i \sim$ 独立同居 $\mathrm{N} 1\left(0, \sigma_B^2\right)$. 由于 $t$ 观察到的处理水平是从无限数量的处理重复中随机选择的，随机变量有无限数量的可能值 $B T i j$. 假设平均影响 $B T{i j}$ 每个块 为零。但现在 $\mathrm{E}\left[B T_{i j}\right]=0$ 并不意味着 $\sum_{j=1}^t B T_{i j}=0$ 对于每个 $i$ 由于变量 $B T_{i j}$ 有无限的人口。因此，零期望并不意味着依赖。在正态假设下，让 $b t$ 随机变量 $B \bar{T} i j \sim i i d \mathrm{~N}1\left(\overline{0}, \sigma B T^2\right)$. 最后，在每个块处理组合中，假设嵌套重复是从无限群体中抽样的。在正态性和 zèo 期望假设下，让 btr 随机变量 $R(B T)(i j) k \sim$ 独 立同居 $\mathrm{N}_1\left(0, \sigma R(B T)^2\right)$. 此外，假设随机变量 $B_i$, 随机变量 $B T{i j}$, 和随机变量 $R(B T)_{(i j) k}$ 是相互独立的。因此，在不接受限制的模型中，模型右侧的所有变量都被 假定为独立的。Kempthorne (1952) 称此类模型为无限模型，因为假设所有随机分量都是从无限种群中抽样的。

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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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