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# 统计代写|假设检验代考Hypothesis Testing代考|STA2302 The Sample Trimmed Mean

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## 统计代写|假设检验代考Hypothesis Testing代考|The Sample Trimmed Mean

As already indicated, the standard error of the sample mean can be relatively large when sampling from a heavy-tailed distribution, and the sample mean estimates a nonrobust measure of location, $\mu$. The sample trimmed mean addresses these problems.

The sample trimmed mean, which estimates the population trimmed $\mu_t$ (described in Section 2.2.3), is computed as follows. Let $X_1, \ldots, X_n$ be a random sample and let $X_{(1)} \leq X_{(2)} \leq \cdots \leq X_{(n)}$ be the observations written in ascending order. The value $X_{(i)}$ is called the $i$ th-order statistic. Suppose the desired amount of trimming has been chosen to be $\gamma, 0 \leq \gamma<.5$. Let $g=[\gamma n]$, where $[\gamma n]$ is the value of $\gamma n$ rounded down to the nearest integer. For example, $[10.9]=10$. The sample trimmed mean is computed by removing the $g$ largest and $g$ smallest observations and averaging the values that remain. In symbols, the sample trimmed mean is
$$\bar{X}t=\frac{X{(g+1)}+\cdots+X_{(n-g)}}{n-2 g} .$$
In essence, the empirical distribution is trimmed in a manner consistent with how the probability density function was trimmed when defining $\mu_t$. As indicated in Chapter 2, two-sided trimming is assumed unless stated otherwise.
The definition of the sample trimmed mean given by Eq. (3.1) is the one most commonly used. However, for completeness, it is noted that the term trimmed mean sometimes refers to a slightly different estimator (e.g., Reed, 1998; cf. Hogg, 1974), namely,
$$\frac{1}{n(1-2 \gamma)}\left(\sum_{i=g+1}^{n-g} X_{(i)}+(g-\gamma n)\left(X_{(g)}+X_{(n-g+1)}\right)\right)$$

## 统计代写|假设检验代考Hypothesis Testing代考|R and S-PLUS Function tmean

Because it is common to use $20 \%$ trimming, for convenience the R (and S-PLUS) function
$$\operatorname{tmean}(\mathrm{x}, \mathrm{tr}=.2)$$
has been supplied, which computes a $20 \%$ trimmed mean by default using the data stored in the S-PLUS vector $\mathrm{x}$. Here, $\mathrm{x}$ can be any $\mathrm{R}$ or S-PLUS vector containing data. The amount of trimming can be altered using the argument $t r$. So tmean (blob) will compute a $20 \%$ trimmed mean for the data stored in blob, and tmean (blob, tr=.3) will use $30 \%$ trimming instead. For convenience, the function
$$11 \text { oc }(x, \text { est=tmean }, \ldots)$$
is supplied for computing a trimmed mean when data are stored in list mode or a matrix. If $x$ is a matrix, lloc computes the trimmed mean for each column. Other measures of location can be used via the argument est. (For example, est=median will compute the median.) The argument … means that any optional arguments associated with est can be used.

## 统计代写|假设检验代考Hypothesis Testing代考|The Sample Trimmed Mean

$\gamma, 0 \leq \gamma<.5$. 让 $g=[\gamma n]$ ，在哪里 $[\gamma n]$ 是价值 $\gamma n$ 四舍五入到最接近的整数。例如， $[10.9]=10$. 样本修剪均值是通过删除 $g$ 最 大的和 $g$ 最小的观测值并对剩余的值进行平均。在符号中，样本修剪平圴值是
$$\bar{X} t=\frac{X(g+1)+\cdots+X_{(n-g)}}{n-2 g} .$$

$$\frac{1}{n(1-2 \gamma)}\left(\sum_{i=g+1}^{n-g} X_{(i)}+(g-\gamma n)\left(X_{(g)}+X_{(n-g+1)}\right)\right)$$

## 统计代写|假设检验代考Hypothesis Testing代考|R and S-PLUS Function tmean

$$\operatorname{tmean}(\mathrm{x}, \mathrm{tr}=.2)$$

$$11 \text { oc }(x, \text { est }=\operatorname{tmean}, \ldots)$$

## 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。