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# 统计代写|抽样理论代考Sampling Theory代写|STATS3003 DEFINITIONS AND TERMINOLOGIES

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## 统计代写|抽样理论代考Sampling Theory代写|Noninformative and Adaptive (Sequential) Sampling Designs

A sampling design $p$ is said to be noninformative if the selection probability $p(s)$ of a sample $s$ does not depend on the value of the study variable $\gamma$. In adaptive or sequential sampling procedures, the selection probability $p(s)$ may depend on the values of the variable of interest $y$ for the units selected in the sample $s$.
Estimator and Estimate
After selection of a sample $s$ using a suitable sampling design $p$, information on the study variable $\gamma$ is collected from each of the units selected in the sample. Here we assume that all units in the sample have responded and there is no measurement error in measuring a response, i.e., the true value $y_i$, of the study variable $y$ is obtained from each of the $i$ th unit $(i \in s)$. The information gathered from the selected units in the sample and their values $y_i$ ‘s is known as data, and it will be denoted by $d=\left(\left(i, \gamma_i\right), i \in s\right)$. The collection of all possible values of $d$ is known as the sample space, and it will be denoted by $\mathscr{X}$. A real valued function $T(s, \mathbf{y})=T(d)$ of $d$ on the sample space $\mathscr{X}$ is known as a statistic. When the statistic $T(s, \mathbf{y})$ is used as a guess value of a certain parametric function $\theta=\theta(\mathbf{y})$ of interest (such as the population mean, total, median etc.), we call $T(s, \mathbf{y})$ as an estimator of the parameter $\theta$. Obviously, an estimator is a random variable whose value depends on the sample selected (i.e., data). The numerical value of an estimator for a given data is called an estimate.

## 统计代写|抽样理论代考Sampling Theory代写|Unbiased Estimator

An estimator $T=T(s, y)$ is said to be design unbiased ( $p$-unbiased or unbiased) for estimating a population parameter $\theta$ if and only if
$$E_p(T)=\sum_{s \in \mathcal{J}} T(s, \mathbf{y}) p(s)=\theta \quad \forall \quad \mathbf{y} \in R^N$$
where, $E_p$ denotes the expectation with respect to the sampling design $p$, $p(s)$ is the probability of the selection of the sample $s$ according to design $p, \mathcal{S}$ is the collection of all possible samples, and $R^N$ is the $N$-dimensional Euclidean space. The class of all unbiased estimators of $\theta$ satisfying (2.2.1) will be denoted by $C_\theta$.

An estimator, which is not unbiased, is called a biased (or design biased) estimator. The amount of bias of an estimator $T$ is defined as
$$B(T)=E_p(T)-\theta=\sum_{s \in \mathcal{J}} T(s, \mathbf{y}) p(s)-\theta$$

# 抽样理论代写

## 统计代写|抽样理论代考Sampling Theory代写|Unbiased Estimator

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$$E_p(T)=\sum_{s \in \mathcal{J}} T(s, \mathbf{y}) p(s)=\theta \quad \forall \quad \mathbf{y} \in R^N$$

## 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。