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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写计量经济学Econometrics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。我们的专家在代写计量经济学Econometrics代写方面经验极为丰富，各种代写计量经济学Econometrics相关的作业也就用不着说。

• 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

经济代写|计量经济学代写Econometrics代考|Size and Power

We introduced the concepts of the size and the power of hypothesis tests in Section 3.4. One way to see how these concepts are related is to study the size-power tradeoff curve for any given test. For simplicity, let us consider a test statistic that is always a positive number (test statistics which are asymptotically distributed as $F$ or $\chi^2$ under the null hypothesis should have this property). If we choose a critical value of zero, the test will always reject the null, whether or not the DGP is actually a special case of the null. As we choose larger and larger critical values, the probability that the test will reject the null will decrease. If the test is a useful one, this probability will initially decrease much less rapidly when the null is false than when it is true. The size-power tradeoff curve shows, for some given sample size, these two probabilities graphed against each other. The horizontal axis shows the size, computed for a DGP that satisfies the null hypothesis, and the vertical axis shows the power, for some other given DGP that will not in general satisfy it. Thus the tradeoff curve shows what the power of the test against the given DGP is for every size of test that we may choose.

Now consider Figure 12.1, which shows several size-power tradeoff curves for different hypothetical test statistics. The horizontal axis measures size. The vertical axis measures power, when the data are generated by a given DGP. The size-power tradeoff curve is generated by varying the critical value for the test. The upper right-hand corner of the graph corresponds to a critical value of zero. Both size and power are 1 at this point. The lower left-hand corner corresponds to a very large critical value, so large that the test statistic will never exceed it. Both size and power are 0 at this point. For many test statistics, such as those that have $\chi^2$ distributions under the null, this latter critical value is in principle plus infinity. However, we could easily pick a finite critical value such that the test statistic would exceed it with probability as close to zero as we chose.

经济代写|计量经济学代写Econometrics代考|Drifting DGPs

In order to determine any of the statistical properties of a test, one must specify how the data are actually generated. Since, in this chapter, we are concerned solely with tests in regression directions, we will restrict our attention to DGPs that differ from the null hypothesis only in such directions. This restriction is by no means innocuous. It means that we cannot say anything about the power of tests in regression directions when the model is false in a nonregression direction (e.g., when the error terms suffer from unmodeled heteroskedasticity). Some aspects of this topic will be discussed in Chapter 16.
The natural way to specify a DGP for the purpose of analyzing the power of a test is to assume that it is a particular member of the set of DGPs which together form the alternative hypothesis. There are two problems with this simple approach, however. The first problem is that one may well be interested in the power of certain tests when the data are generated by a DGP which is not a special case of the alternative hypothesis. It does not make sense to rule out this interesting case.

The second problem, which we alluded to in the previous section, is that most test statistics that are of interest to us will have no nondegenerate asymptotic distribution under a fixed DGP that is not a special case of the null hypothesis. If they did, then they would not be consistent. One long-standing solution to this problem is to consider the distribution of the test statistic of interest under what is called a sequence of local alternatives. When $\boldsymbol{\theta}$ is the parameter vector of interest, such a sequence may be written as
$$\boldsymbol{\theta}^n=\boldsymbol{\theta}_0+n^{-1 / 2} \boldsymbol{\delta} .$$
Here $\boldsymbol{\theta}^n$ is the parameter vector for a sample of size $n, \boldsymbol{\theta}_0$ is a parameter vector that satisfies the null hypothesis, and $\boldsymbol{\delta}$ is some nonzero vector. Evidently, $\boldsymbol{\theta}^n$ approaches $\theta_0$ at a rate proportional to $n^{-1 / 2}$. The originator of this device was Neyman (1937). However, it is often attributed to Pitman (1949) and is therefore sometimes referred to as a “Pitman sequence” or “Pitman drift”; see McManus (1991). This technique has been widely used in econometric theory; see, for example, Gallant and Holly (1980) and Engle (1984).

In order to avoid ruling out the interesting case in which the data are generated by a DGP that is not a special case of the alternative hypothesis, Davidson and MacKinnon (1985a, 1987) generalized the idea of sequences of local alternatives to the idea of drifting DGPs. This chapter is largely based on the approach of those two papers. ${ }^2$

计量经济学代考

经济代写|计量经济学代写Econometrics代考|Drifting DGPs

$$\boldsymbol{\theta}^n=\boldsymbol{\theta}_0+n^{-1 / 2} \boldsymbol{\delta} .$$

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