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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|Efficiency and BLUEness

Under assumptions 5 and 6 , we can prove that the OLS estimators are the most efficient among all unbiased linear estimators. Thus we can conclude that the OLS procedure yields BLU estimators.

The proof that the OLS estimators are BLU estimators is relatively complicated. It entails a procedure which goes the opposite way from that followed so far. We start the estimation from the beginning, trying to derive a BLU estimator of $\beta$ based on the properties of linearity, unbiasedness and minimum variance one by one, and then we check whether the BLU estimator derived by this procedure is the same as the OLS estimator.

Thus, we want to derive the BLU estimator of $\beta$, say $\breve{\beta}$, concentrating first on the property of linearity. For $\breve{\beta}$ to be linear we need to have:
$$\breve{\beta}=\delta_{1} Y_{1}+\delta_{2} Y_{2}+\cdots+\delta_{n} Y_{n}=\sum \delta_{t} Y_{t}$$
where the $\delta_{t}$ terms are constants, the values of which are to be determined.
Proceeding with the property of unbiasedness, for $\breve{\beta}$ to be unbiased we must have $E(\breve{\beta})=\beta .$ We know that:
$$E(\breve{\beta})=E\left(\sum \delta_{t} Y_{t}\right)=\sum \delta_{t} E\left(Y_{t}\right)$$

## 经济代写|计量经济学代写Econometrics代考|The overall goodness of fit

We showed earlier that the regression equation obtained from the OLS method fits a scatter diagram quite closely. However, we need to know how close it is to the scattered observed values to be able to judge whether one particular line describes the relationship between $Y_{t}$ and $X_{t}$ better than an alternative line. In other words, it is desirable to know a measure that describes the closeness of fit. This measure will also inform us how well the equation we have obtained accounts for the behaviour of the dependent variable.

To obtain such a measure, we first have to decompose the actual value of $Y_{t}$ into a predicted value, which comes from the regression equation, $\hat{Y}{t}$, plus the equation’s residuals: $$Y{t}=\hat{Y}{t}+\hat{u}{t}$$
Subtracting $\bar{Y}$ from both sides we have:
$$Y_{t}-\bar{Y}=\hat{Y}{t}-\bar{Y}+\hat{u}{t}$$
We need to obtain a measure of the total variation in $Y_{t}$ from its mean $\bar{Y}$. Therefore, we take the sum of Equation (3.58):
$$\sum\left(Y_{t}-\bar{Y}\right)=\sum\left(\hat{Y}{t}-\bar{Y}+\hat{u}{t}\right)$$
then square both terms to get:
$$\sum\left(Y_{t}-\bar{Y}\right)^{2}=\sum\left(\hat{Y}{t}-\bar{Y}+\hat{u}{t}\right)^{2}$$
Note that, if we divided the measure on the left-hand side of the above equation by $n$, we would simply get the sample variance of $Y_{t}$. So $\sum\left(Y_{t}-\bar{Y}\right)^{2}$ is an appropriate measure of the total variation in $Y_{t}$, often called the total sum of squares (TSS).

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|Efficiency and BLUEness

OLS 估计器是 BLU 估计器的证明相对复杂。它需要一个与迄今为止所遵循的相反的过程。我们从一开始就开始估计，试图推导出一个 BLU 估计量 $\beta$ 根据线性、无 偏性和最小方差的性质，我们一一检查通过该程序导出的 BLU 估计量是否与 OLS 估计量相同。

$$\breve{\beta}=\delta_{1} Y_{1}+\delta_{2} Y_{2}+\cdots+\delta_{n} Y_{n}=\sum \delta_{t} Y_{t}$$

$$E(\breve{\beta})=E\left(\sum \delta_{t} Y_{t}\right)=\sum \delta_{t} E\left(Y_{t}\right)$$

## 经济代写|计量经济学代写Econometrics代考|The overall goodness of fit

$$Y t=\hat{Y} t+\hat{u} t$$

$$Y_{t}-\bar{Y}=\hat{Y} t-\bar{Y}+\hat{u} t$$

$$\sum\left(Y_{t}-\bar{Y}\right)=\sum(\hat{Y} t-\bar{Y}+\hat{u} t)$$

$$\sum\left(Y_{t}-\bar{Y}\right)^{2}=\sum(\hat{Y} t-\bar{Y}+\hat{u} t)^{2}$$

## 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