### 统计代写|抽样调查作业代写sampling theory of survey代考|STAT 506

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• 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

## 统计代写|抽样调查作业代写sampling theory of survey代考|Preliminaries and Basics of Probability Sampling

Various government organizations, researchers, sociologist, and businesses often conduct surveys to get answers to certain specific questions, which cannot be obtained merely through laboratory experiments or simply using economic, mathematical, or statistical formulation. For example, the knowledge of the proportion of unemployed people, those below poverty line, and the extent of child labor in a certain locality is very important for the formulation of a proper economic planning. To get the answers to such questions, we conduct surveys on sections of people of the locality very often. Surveys should be conducted in such a way that the results of the surveys can be interpreted objectively in terms of probability. Drawing inference about aggregate (population) on the basis of a sample, a part of the populations, is a natural instinct of human beings. Surveys should be conducted in such a way that the inference relating to the population should have some valid statistical background. To achieve valid statistical inferences, one needs to select samples using some suitable sampling procedure. The collected data should be analyzed appropriately. In this book, we have discussed various methods of sample selection procedures, data collection, and methods of data analysis and their applications under various circumstances. The statistical theories behind such procedures have also been studied in great detail.

In this chapter we introduce some of the basic definitions and terminologies in survey sampling such as population, unit, sample, sampling designs, and sampling schemes. Various methods of sample selection as well as Hanurav’s algorithm which gives the correspondence between a sampling design and a sampling scheme have also been discussed.

## 统计代写|抽样调查作业代写sampling theory of survey代考|Parameter and Parameter Space

For a given population $U$, we may be interested in studying certain characteristics of it. Such characteristics are known as study variables. When considering a population of students in a certain class, we may be interested to know the age, height, racial group, economic condition, marks on different subjects, and so forth. Each of the variables under study is called a study variable, and it will be denoted by $\gamma$. Let $\gamma_{i}$ be the value of a study variable $y$ for the $i$ th unit of the population $U$, which is generally not known before the survey. The $N$-dimension vector $\mathbf{y}=\left(\gamma_{1}, \ldots, \gamma_{i}, \ldots, \gamma_{\mathrm{N}}\right)$ is known as a parameter of the population $U$ with respect to the characteristic $\gamma$. The set of all-possible values of the vector $\mathbf{y}$ is the $N$-dimensional Euclidean space $R^{N}=\left(-\infty<y_{1}<\infty, \ldots,-\infty<\gamma_{i}<\infty, \ldots,-\infty<\gamma_{N}<\infty\right)$ and it is known as a parameter space. In most of the cases we are not interested in knowing the parameter $\mathbf{y}$ but in a certain parametric function of $\mathbf{y}$ such as, $Y=\sum_{i=1}^{N} \gamma_{i}=$ population total, $\bar{Y}=\frac{1}{N} \sum_{i=1}^{N} \gamma_{i}=$ population mean, $S_{Y}^{2}=\frac{1}{N-1} \sum_{i=1}^{N}\left(y_{i}-\bar{Y}\right)^{2}=$ population variance, $C_{\gamma}=S_{Y} / \bar{Y}$ $=$ population coefficient of variation, and so forth.

## 广义线性模型代考

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## MATLAB代写

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