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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
• 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|The Geometry of Nonlinear Least Squares

By far the most common way to estimate nonlinear as well as linear regression models is to minimize the sum of squared residuals, or $\mathrm{SSR}$, as a function of $\boldsymbol{\beta}$. For the model (2.01), the sum-of-squares function is
$$\operatorname{SSR}(\boldsymbol{\beta})=\sum_{t=1}^{n}\left(y_{t}-x_{t}(\boldsymbol{\beta})\right)^{2} .$$
It is usually more convenient to write this in matrix notation as
$$S S R(\boldsymbol{\beta})=(\boldsymbol{y}-\boldsymbol{x}(\boldsymbol{\beta}))^{\top}(\boldsymbol{y}-\boldsymbol{x}(\boldsymbol{\beta}))$$
where $\boldsymbol{y}$ is an $n$-vector of observations $y_{t}$ and $\boldsymbol{x}(\boldsymbol{\beta})$ is an $n$-vector of regression functions $x_{t}(\boldsymbol{\beta})$. As we saw in Chapter 1 , another notation, which is perhaps not so convenient to work with algebraically but is more compact and emphasizes the geometry involved, is
$$S S R(\boldsymbol{\beta})=|\boldsymbol{y}-\boldsymbol{x}(\boldsymbol{\beta})|^{2},$$
where $|\boldsymbol{y}-\boldsymbol{x}(\boldsymbol{\beta})|$ is the length of the vector $\boldsymbol{y}-\boldsymbol{x}(\boldsymbol{\beta})$. Expression (2.03) makes it clear that when we minimize $\operatorname{SSR}(\boldsymbol{\beta})$, we are in fact minimizing the Euclidean distance between $\boldsymbol{y}$ and $\boldsymbol{x}(\boldsymbol{\beta})$, an interpretation that we will discuss at length below.
The sum-of-squares function (2.02) can be rewritten as
$$\operatorname{SSR}(\boldsymbol{\beta})=\boldsymbol{y}^{\top} \boldsymbol{y}-2 \boldsymbol{y}^{\top} \boldsymbol{x}(\boldsymbol{\beta})+\boldsymbol{x}^{\top}(\boldsymbol{\beta}) \boldsymbol{x}(\boldsymbol{\beta}) .$$

## 经济代写|计量经济学代写Econometrics代考|Identification in Nonlinear Regression Models

If we are to minimize $S S R(\boldsymbol{\beta})$ successfully, it is necessary that the model be identified. Identification is a geometrically simple concept that applies to a very wide variety of models and estimation techniques. Unfortunately, the term identification has come to be associated in the minds of many students of econometrics with the tedious algebra of the linear simultaneous equations model. Identification is indeed an issue in such models, and there are some special problems that arise for them (see Chapters 7 and 18), but the concept is applicable to every econometric model. Essentially, a nonlinear regression model is identified by a given data set if, for that data set, we can find a unique $\hat{\boldsymbol{\beta}}$ that minimizes $\operatorname{SSR}(\boldsymbol{\beta})$. If a model is not identified by the data being used, then there will be more than one $\hat{\boldsymbol{\beta}}$, perhaps even an infinite number of them. Some models may not be identifiable by any conceivable data set, while other models may be identified by some data sets but not by others.

There are two types of identification, local and global. The least squares estimate $\hat{\boldsymbol{\beta}}$ will be locally identified if whenever $\hat{\boldsymbol{\beta}}$ is perturbed slightly, the value of $S S R(\boldsymbol{\beta})$ increases. This may be stated formally as the requirement that the function $\operatorname{SSR}(\boldsymbol{\beta})$ be strictly convex at $\hat{\boldsymbol{\beta}}$. Thus
$$\operatorname{SSR}(\hat{\boldsymbol{\beta}})<\operatorname{SSR}(\hat{\boldsymbol{\beta}}+\boldsymbol{\delta})$$
for all “small” perturbations $\boldsymbol{\delta}$.

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|The Geometry of Nonlinear Least Squares

$$\operatorname{SSR}(\boldsymbol{\beta})=\sum_{t=1}^{n}\left(y_{t}-x_{t}(\boldsymbol{\beta})\right)^{2} .$$

$$\operatorname{SSR}(\boldsymbol{\beta})=(\boldsymbol{y}-\boldsymbol{x}(\boldsymbol{\beta}))^{\top}(\boldsymbol{y}-\boldsymbol{x}(\boldsymbol{\beta}))$$

$$S S R(\boldsymbol{\beta})=|\boldsymbol{y}-\boldsymbol{x}(\boldsymbol{\beta})|^{2},$$

$$\operatorname{SSR}(\boldsymbol{\beta})=\boldsymbol{y}^{\top} \boldsymbol{y}-2 \boldsymbol{y}^{\top} \boldsymbol{x}(\boldsymbol{\beta})+\boldsymbol{x}^{\top}(\boldsymbol{\beta}) \boldsymbol{x}(\boldsymbol{\beta}) .$$

## 经济代写|计量经济学代写Econometrics代考|Identification in Nonlinear Regression Models

$$\operatorname{SSR}(\hat{\boldsymbol{\beta}})<\operatorname{SSR}(\hat{\boldsymbol{\beta}}+\boldsymbol{\delta})$$

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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