### 经济代写|计量经济学代写Econometrics代考|ECON2300

statistics-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|Central limit theorem

If a set of data is iid with $n$ observations, $\left(\mathrm{Y}_1, \mathrm{Y}_2, \ldots \mathrm{Y}_n\right)$, and with a finite variance then as $n$ goes to infinity the distribution of $\bar{Y}$ becomes normal. So as long as $n$ is reasonably large we can think of the distribution of the mean as being approximately normal.

This is a remarkable result; what it says is that, regardless of the form of the population distribution, the sampling distribution will be normal as long as it is based on a large enough sample. To take an extreme example, suppose we think of a lottery which pays out one winning ticket for every 100 tickets sold. If the prize for a winning ticket is $\$ 100$and the cost of each ticket is$\$1$, then, on average, we would expect to earn $\$ 1$per ticket bought. But the population distribution would look very strange; 99 out of every 100 tickets would have a return of zero and one ticket would have a return of$\$100$. If we tried to graph the distribution of returns it would have a huge spike at zero and a small spike at $\$ 100$and no observations anywhere else. But, as long as we draw a reasonably large sample, when we calculate the mean return over the sample it will be centred on$\$1$ with a normal distribution around 1 .

The importance of the central limit theorem is that it allows us to know what the sampling distribution of the mean should look like as long as the mean is based on a reasonably large sample. So we can now replace the arbitrary triangular distribution in Figure 1.1 with a much more reasonable one, the normal distribution.

A final small piece of our statistical framework is the law of large numbers. This simply states that if a sample $\left(\mathrm{Y}_1, \mathrm{Y}_2, \ldots \mathrm{Y}_n\right)$ is IID with a finite variance then $\bar{Y}$ is a consistent estimator of $\mu$, the true population mean. This can be formally stated as $\operatorname{Pr}(|\bar{Y}-\mu|<\varepsilon) \rightarrow 1$ as $n \rightarrow \infty$, meaning that the probability that the absolute difference between the mean estimate and the true population mean will be less than a small positive number tends to one as the sample size tends to infinity. This can be proved straightforwardly, since, as we have seen, the variance of the sampling distribution of the mean is inversely proportional to $n$; hence as $n$ goes to infinity the variance of the sampling distribution goes to zero and the mean is forced to the true population mean.

We can now summarize: $\bar{Y}$ is an unbiased and consistent estimate of the true population mean $\mu$; it is approximately distributed as a normal distribution with a variance which is inversely proportional to $n$; this may be expressed as $N\left(\mu, \sigma^2 / n\right)$. So if we subtract the population mean from $\bar{Y}$ and divide by its standard deviation we will create a variable which has a mean of zero and a unit variance. This is called standardizing the variable.

## 经济代写|计量经济学代写Econometrics代考|Cross-sectional data

A cross-sectional data set consists of a sample of individuals, households, firms, cities, countries, regions or any other type of unit at a specific point in time. In some cases, the data across all units do not correspond to exactly the same time period. Consider a survey that collects data from questionnaire surveys of different families on different days within a month. In this case, we can ignore the minor time differences in collection and the data collected will still be viewed as a cross-sectional data set.

In econometrics, cross-sectional variables are usually denoted by the subscript $i$, with $i$ taking values of $1,2,3, \ldots, N$, for $N$ number of cross-sections. So if, for example, $Y$ denotes the income data we have collected for $N$ individuals, this variable, in a cross-sectional framework, will be denoted by:
$$Y_i \quad \text { for } i=1,2,3, \ldots, N$$
Cross-sectional data are widely used in economics and other social sciences. In economics, the analysis of cross-sectional data is associated mainly with applied microeconomics. Labour economics, state and local public finance, business economics, demographic economics and health economics are some of the prominent fields in microeconomics. Data collected at a given point in time are used in these cases to test microeconomic hypotheses and evaluate economic policies.

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|Cross-sectional data

$$Y_i \quad \text { for } i=1,2,3, \ldots, N$$

## 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。