### 英国补考|抽样调查作业代写sampling theory of survey代考|MATH 525

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• 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

## 英国补考|抽样调查作业代写sampling theory of survey代考|Sampling and Nonsampling Errors

Obviously, using the complete enumeration method, we get the correct value of the parameter, provided all the $\gamma$-values of the population obtained are correct. This would mean that there is no nonresponse, i.e., a response from each unit is obtained, and there is no measurement error in measuring $\gamma$-values. However, in practice, at least for a large-scale survey, nonresponse is unavoidable, and $\gamma$-values are also subject to error because the respondents report untrue values, especially when $\gamma$-values relate to confidential characteristics such as income and age. The error in a survey, which is originated from nonresponse or incorrect measurement of $y$-values, is termed as the nonsampling error. The nonsampling errors increase with the sample size.
From a sample survey, we cannot get the true value of the parameter because we surveyed only a sample, which is just a part of the population. The error committed by making inference by surveying a part of the population is known as the sampling error. In complete enumeration,sampling error is absent, but it is subjected more to nonsampling error than sample surveys. When the population is large, complete enumeration is not possible as it is very expensive, time-consuming, and requires many trained investigators. The advantages of sample surveys over complete enumeration were advocated by Mahalanobis (1946), Cochran (1977), and Murthy (1977), to name a few.

## 英国补考|抽样调查作业代写sampling theory of survey代考|Cumulative Total Method

Here we label all possible samples of $\mathcal{S}$ as $s_{1}, \ldots, s_{i}, \ldots, s_{M}$, where $M=$ total number of samples in $\mathscr{e}$. Then we calculate the cumulative total $T_{i}=p\left(s_{1}\right)+\cdots+p\left(s_{i}\right)$ for $i=1, \ldots, M$ and select a random sample $R$ (say) from a uniform population with range $(0,1)$. This can be done by choosing a five-digit random number and placing a decimal preceding it. The sample $s_{k}$ is selected if $T_{k-1}<R \leq T_{k}$, for $k=1, \ldots, M$ with $T_{0}=0$.

Example $1.4 .1$
Let $U=(1,2,3,4) ; s_{1}=(1,1,2), s_{2}=(1,2,2), s_{3}=(3,2), s_{4}=(4)$; $p\left(s_{1}\right)=0.25, p\left(s_{2}\right)=0.30, p\left(s_{3}\right)=0.20$, and $p\left(s_{4}\right)=0.25$.
$\begin{array}{lllll}s & s_{1} & s_{2} & s_{3} & s_{4} \ p(s) & 0.25 & 0.30 & 0.20 & 0.25 \ T_{k} & 0.25 & 0.55 & 0.75 & 1\end{array}$
Let a random sample $R=0.34802$ be selected from a uniform population with range $(0,1)$. The sample $s_{2}$ is selected as $T_{1}=0.25<R=$ $0.34802 \leq T_{2}=0.55$.

The cumulative total method mentioned above, however, cannot be used in practice because here we have to list all the possible samples having positive probabilities. For example, suppose we need to select a sample of size 15 from a population size $R=30$ following a sampling design, where all possible samples of size $n=15$ have positive probabilities, we need to list $M=\left(\begin{array}{l}30 \ 15\end{array}\right)$ possible samples, which is obviously a huge number.

## 英国补考|抽样调查作业代写sampling theory of survey代考|Cumulative Total Method

$p\left(s_{1}\right)=0.25, p\left(s_{2}\right)=0.30, p\left(s_{3}\right)=0.20$ ，和 $p\left(s_{4}\right)=0.25$.

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