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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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

## 经济代写|计量经济学代写Econometrics代考|Models and Data-Generating Processes

The continuity of the regression function implies that a model incorporating the regression function (2.07) will be poorly identified whenever the true value of either $\beta_{2}$ or $\beta_{3}$ is close, but not actually equal, to zero. In fact, it is likely to be poorly identified even for values of these parameters that are far from zero, because, for most sets of data on $z_{t}$, the Hessian for this model will be fairly close to singular. As we will demonstrate in Chapter 5 , for nonlinear regression models the Hessian $\boldsymbol{H}(\boldsymbol{\beta})$ is, for values of $\boldsymbol{\beta}$ near $\hat{\boldsymbol{\beta}}$, generally approximated quite well by the matrix
$$2 \boldsymbol{X}^{\top}(\boldsymbol{\beta}) \boldsymbol{X}(\boldsymbol{\beta})$$
For the regression function (2.07), the $t^{\mathrm{th}{1}}$ row of the matrix $\boldsymbol{X}(\boldsymbol{\beta})$ is $$\left[\begin{array}{lll} 1 & z{t}^{\beta_{3}} & \beta_{2} z_{t}^{\beta_{3}} \log \left(z_{t}\right) \end{array}\right] .$$
The third column of $\boldsymbol{X}(\boldsymbol{\beta})$ is thus very similar to the second column, each element of the latter being equal to the corresponding element of the former times a constant and $\log \left(z_{t}\right)$. Unless the range of $z_{t}$ is very great, or there are some values of $z_{t}$ very close to zero, $z_{t}^{\beta_{3}}$ and $\beta_{2} z_{t}^{\beta_{3}} \log \left(z_{t}\right)$ will tend to be very highly correlated. Thus the matrix $\boldsymbol{X}^{\top}(\boldsymbol{\beta}) \boldsymbol{X}(\boldsymbol{\beta})$, and hence in most cases the Hessian as well, will often be close to singular. This example will be discussed in more detail in Chapter $6 .$

## 经济代写|计量经济学代写Econometrics代考|Models and Data-Generating Processes

In economics, it is probably not often the case that a relationship like (2.01) actually represents the way in which a dependent variable is generated, as it might if $x_{t}(\boldsymbol{\beta})$ were a physical response function and $u_{t}$ merely represented errors in measuring $y_{t}$. Instead, it is usually a way of modeling how $y_{t}$ varies with the values of certain variables. They may be the only variables about which we have information or the only ones that we are interested in for a particular purpose. If we had more information about potential explanatory variables, we might very well specify $x_{t}(\boldsymbol{\beta})$ differently so as to make use of that additional information.

It is sometimes desirable to make explicit the fact that $x_{t}(\boldsymbol{\beta})$ represents the conditional mean of $y_{t}$, that is, the mean of $y_{t}$ conditional on the values of a number of other variables. The set of variables on which $y_{t}$ is conditioned is often referred to as an information set. If $\Omega_{t}$ denotes the information set on which the expectation of $y_{t}$ is to be conditioned, one could define $x_{t}(\boldsymbol{\beta})$ formally as $E\left(y_{t} \mid \Omega_{t}\right)$. There may be more than one such information set. Thus we might well have both
$$x_{1 t}\left(\boldsymbol{\beta}{1}\right) \equiv E\left(y{t} \mid \Omega_{1 t}\right) \quad \text { and } \quad x_{2 t}\left(\boldsymbol{\beta}{2}\right) \equiv E\left(y{t} \mid \Omega_{2 t}\right),$$
where $\Omega_{1 t}$ and $\Omega_{2 t}$ denote two different information sets. The functions $x_{1 t}\left(\boldsymbol{\beta}{1}\right)$ and $x{2 t}\left(\boldsymbol{\beta}_{2}\right)$ might well be quite different, and we might want to estimate both of them for different purposes. There are many circumstances in which we might not want to condition on all available information. For example, if the ultimate purpose of specifying a regression function is to use it for forecasting, there may be no point in conditioning on information that will not be available at the time the forecast is to be made.

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|Models and Data-Generating Processes

$$2 \boldsymbol{X}^{\top}(\boldsymbol{\beta}) \boldsymbol{X}(\boldsymbol{\beta})$$

$$\left[\begin{array}{lll} 1 & z t^{\beta_{3}} & \beta_{2} z_{t}^{\beta_{3}} \log \left(z_{t}\right) \end{array}\right] .$$

## 经济代写|计量经济学代写Econometrics代考|Models and Data-Generating Processes

$$x_{1 t}(\beta 1) \equiv E\left(y t \mid \Omega_{1 t}\right) \quad \text { and } \quad x_{2 t}(\beta 2) \equiv E\left(y t \mid \Omega_{2 t}\right),$$

## 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。

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