19th Ave New York, NY 95822, USA

# 统计代写|Generalized linear model代考广义线性模型代写|The General Linear Model

my-assignmentexpert™广义线性模型Generalized linear model作业代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。my-assignmentexpert™， 最高质量的广义线性模型Generalized linear model作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此广义线性模型Generalized linear model作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

my-assignmentexpert™ 为您的留学生涯保驾护航 在统计Statistics作业代写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。我们的专家在广义线性模型Generalized linear model代写方面经验极为丰富，各种广义线性模型Generalized linear model相关的作业也就用不着 说。

## 统计代写|Generalized linear model代考广义线性模型代写|Model definition and examples

Given data $\left(Y_{i}, X_{i 1}, X_{i 2}, \cdots, X_{i k}\right), i=1, \cdots, N$, the general linear model has the form
$$\mathbf{y}=\mathbf{X} \beta+\varepsilon$$
where $\mathbf{y}=\left(Y_{1}, \cdots, Y_{N}\right)^{\prime}$ is an $N$-dimensional vector of observed responses, $\beta=$ $\left(\beta_{0}, \beta_{1}, \cdots, \beta_{k}\right)^{\prime}$ is a $(k+1)$-dimensional vector of unknown parameters, $\mathbf{X}$ is an $N \times(k+1)$ matrix of rank $r$ of known predictors, and $\varepsilon=\left(\varepsilon_{1}, \cdots, \varepsilon_{N}\right)^{\prime}$ is an $N$-dimensional random vector of unobserved errors. The matrix $\mathbf{X}$ is written as
$$\mathbf{X}=\left(\begin{array}{cccc} 1 & X_{11} & \cdots & X_{1 k} \ 1 & X_{21} & \cdots & X_{2 k} \ \vdots & \vdots & \vdots & \vdots \ 1 & X_{N 1} & \cdots & X_{N k} \end{array}\right)$$

## 统计代写|Generalized linear model代考广义线性模型代写|The least squares approach

Given data on the response variable and predictors, either from an observational study or from a designed experiment, the objective is inference on the model parameters, or functions of the model parameters, as well as predictions for the response variable based on the general linear model (4.1.1). The method of least squares, which was introduced in the early 19 th century, enables such inference using minimal assumptions. In particular, we need not specify any parametric form for the probability distribution of the errors $\varepsilon_{i}$. In the full rank linear model, i.e., when $r(\mathbf{X})=p$, the least squares approach enables us to construct the best linear unbiased estimator of the parameter vector $\beta$, “best” in the sense of having minimum variance in the class of all linear unbiased estimators. When $r(\mathbf{X})=r<p$, we will obtain least squares estimates of certain linear functions of $\beta$, although, as we shall see, there does not exist a unique estimator for $\beta$ itself. In order to proceed with inference beyond point estimation and prediction for the linear model, i.e., in order to construct confidence interval estimates or to do hypothesis tests, it is usual to assume some parametric form for the error distribution. The simplest and most popular distributional assumption is the assumption of normality of the linear model errors. In Chapter 5 , we introduce suitable families of multivariate probability distributions, including the multivariate normal distribution, and return to classical inference for linear models in Chapter 7 . We now describe the least squares principle.

## 统计代写|GENERALIZED LINEAR MODEL代考广义线性模型代写|Estimable functions

In the previous section, we saw that unless $r(\mathbf{X})=p, \beta^{0}$ is not unique. Although in the full rank model, we can estimate any function of $\beta$, we must restrict our-selves to estimating only certain linear functions of $\beta$ when $r(\mathbf{X})<p$. Such a linear function of $\beta$ is called an estimable function. In other words, a linear function of $\beta$ for which a (unique) estimator based on $\beta^{0}$ exists, which is invariant to the solution $\beta^{0}$, is called an estimable function. A more precise definition, which also provides an approach for the identification of an estimable function of $\beta$, is given below.

A linear parametric function $\mathbf{c}^{\prime} \beta$ is said to be an estimable function of $\beta$ if there exists an $N$-dimensional vector $\mathbf{t}=\left(t_{1}, \cdots, t_{N}\right)^{\prime}$ such that the expectation (with respect to the distribution of $\mathbf{y}$ ) of the linear combination $\mathbf{t}^{\prime} \mathbf{y}=t_{1} Y_{1}+\cdots+t_{N} Y_{N}$ is equal to $\mathbf{c}^{\prime} \beta$, i.e.,
$$E\left(\mathbf{t}^{\prime} \mathbf{y}\right)=\mathbf{c}^{\prime} \beta$$

## 统计代写|GENERALIZED LINEAR MODEL代考广义线性模型代写|MODEL DEFINITION AND EXAMPLES

$$\mathbf{X}=\left(\begin{array}{cccc} 1 & X_{11} & \cdots & X_{1 k} \ 1 & X_{21} & \cdots & X_{2 k} \ \vdots & \vdots & \vdots & \vdots \ 1 & X_{N 1} & \cdots & X_{N k} \end{array}\right)$$

## 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。