如果你也在 怎样代写抽样调查Survey sampling 这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。抽样调查Survey sampling是数学工程这一广泛新兴领域中的一个自然组成部分。例如，我们可以断言，数学工程之于今天的数学系，就像数学物理之于一个世纪以前的数学系一样;毫不夸张地说，数学在诸如语音和图像处理、信息理论和生物医学工程等工程学科中的基本影响。
抽样调查Survey sampling是主流统计的边缘。这里的特殊之处在于，我们有一个具有某些特征的有形物体集合，我们打算通过抓住其中一些物体并试图对那些未被触及的物体进行推断来窥探它们。这种推论传统上是基于一种概率论，这种概率论被用来探索观察到的事物与未观察到的事物之间的可能联系。这种概率不被认为是在统计学中，涵盖其他领域，以表征我们感兴趣的变量的单个值之间的相互关系。但这是由调查抽样调查人员通过任意指定的一种技术从具有预先分配概率的对象群体中选择样本而创建的。
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统计代写|抽样调查作业代写sampling theory of survey代考|ESTIMATION FROM MULTIPLE FRAMES
Suppose a finite population $U$ of size $N$ is covered exactly by the union of two overlapping frames $A$ and $B$ of sizes $N_A$ and $N_B$. Let $E_A$ denote the set of units of $A$ that are not in $B$, $E_{A B}$ denote those that are in both $A$ and $B$, and $E_B$ denote the units of $B$ that are not in $A ; N_{E A}, N_{A B}, N_{E B}$ respectively denote the sizes of these three mutually exclusive sets. Let two samples of sizes $n_A, n_B$ be drawn by SRSWOR from the two lists $A$ and $B$ respectively in independent manners. Let $n_a, n_{a b}, n_{b a}, n_b$ denote respectively the sampled units of $A$ that are in $E_A, E_{A B}$ and of $B$ that are in $E_{A B}, E_B$. Let us denote the corresponding sample means by $\bar{y}a, \bar{y}{a b}, \bar{y}{b a}$, and $\bar{y}_b$. Then for the population total $Y=\sum_1^N Y_i$ one may employ the following estimators $$ \widehat{Y}_1=\left(N{E A} \bar{y}a+N{E B} \bar{y}b\right)+N{A B}\left(p \bar{y}{a b}+q \bar{y}{b a}\right)
$$
if $N_{E A}, N_{E B}$, and $N_{A B}$ are known, or, without this assumption,
$$
\widehat{Y}2=\frac{N_A}{n_A}\left(\bar{y}_a+p \bar{y}{a b}\right)+\frac{N_B}{n_B}\left(\bar{y}b+q \bar{y}{b a}\right)
$$
In $\widehat{Y}1$ and $\widehat{Y}_2, p$ is a suitable number, $0{A B}, E_B$ are known quantities $\sigma_A^2, \sigma_{A B}^2, \sigma_B^2$ and choosing a simple cost function, he gave rules for optimal choices of $n_A, n_B$ subject to a given value of $n=n_A+n_B$ and of $p$.
统计代写|抽样调查作业代写sampling theory of survey代考|Small Domains and Poststratification
Suppose a finite population $U$ of $N$ units labeled $1, \ldots, i, \ldots, N$ consists of a very large, say several thousand, domains of interest, like the households of people of various racial groups of different predominant occupational groups of their principal earning members located in various counties across various states like those in U.S.A. For certain overall general purposes a sample $s$ of a size $n$, which may also be quite large, say a few thousand, may be supposed to have been chosen according to a design $p$ admitting $\pi_i>0$. Then the total $T_d=\sum_{U_d} Y_i$ for a variable of interest $y$ relating to the members of a particular domain $U_d$ of size $N_d$ of interest may be estimated using the direct estimators
$$
t_d=\left(\sum_{s_d} Y_i / \pi_i\right)
$$
or
$$
t_d^{\prime}=N_d\left(\sum_{s_d} Y_i / \pi_i\right) /\left(\sum_{s_d} 1 / \pi_i\right) .
$$
We write $s_d$ for the part of the sample $s$ that coincides with $U_d$, and $n_d$ for the size of $s_d, d=1, \ldots, D$, writing $D$ for the total number of domains such that $U_d$ ‘s are disjoint, coincident with $U$ when amalgamated over all the $U_d$ ‘s $d=1, \ldots, D$. We suppose $D$ is very large and so even for large $n=\sum_{d=1}^D n_d$, the values of $n_d$ for numerous values of $d$ turn out to be quite small, and even nil for many of them. Thus the sample base of $t_d$ or $t_d^{\prime}$ happens in practice to be so small that they may not serve any useful purpose, having inordinately large magnitudes and unstable estimators for their variances, leading to inconsequential confidence intervals, which in most cases fail to cover the true domain totals. Similar and more acute happens to be the problem of estimating the domain means $\bar{T}_d=T_d / N_d$, writing domain size as $N_d$, which often is unknown. Hence the problem of small domain statistics, and a special method of estimation is needed for the parameters relating to small domains, which are often geographical areas and hence are called small areas or local areas. In this section, we will briefly discuss a few issues involved in small area or local area estimation.
抽样调查代考
统计代写|抽样调查作业代写sampling theory of survey代考|ESTIMATION FROM MULTIPLE FRAMES
假设大小为$N$的有限种群$U$被大小为$N_A$和$N_B$的两个重叠帧$A$和$B$的并集完全覆盖。设$E_A$表示$A$中不属于$B$的单位集合，$E_{A B}$表示同时属于$A$和$B$的单位集合，$E_B$表示$B$中不属于$A ; N_{E A}, N_{A B}, N_{E B}$的单位集合，分别表示这三个互斥集合的大小。用SRSWOR分别从$A$和$B$两个列表中独立抽取两个大小为$n_A, n_B$的样本。设$n_a, n_{a b}, n_{b a}, n_b$分别表示位于$E_A, E_{A B}$中的$A$的采样单位和位于$E_{A B}, E_B$中的$B$的采样单位。我们用$\bar{y}a, \bar{y}{a b}, \bar{y}{b a}$和$\bar{y}b$表示相应的样本均值。那么对于人口总数$Y=\sum_1^N Y_i$，可以使用以下估计器$$ \widehat{Y}_1=\left(N{E A} \bar{y}a+N{E B} \bar{y}b\right)+N{A B}\left(p \bar{y}{a b}+q \bar{y}{b a}\right) $$ 如果$N{E A}, N_{E B}$和$N_{A B}$是已知的，或者，没有这个假设，
$$
\widehat{Y}2=\frac{N_A}{n_A}\left(\bar{y}a+p \bar{y}{a b}\right)+\frac{N_B}{n_B}\left(\bar{y}b+q \bar{y}{b a}\right) $$ 在$\widehat{Y}1$和$\widehat{Y}_2, p$是一个合适的数字，$0{A B}, E_B$是已知的数量$\sigma_A^2, \sigma{A B}^2, \sigma_B^2$和选择一个简单的成本函数，他给出了规则的最优选择$n_A, n_B$在给定的值$n=n_A+n_B$和$p$。
统计代写|抽样调查作业代写sampling theory of survey代考|Small Domains and Poststratification
假设一个有限总体 $U$ 的 $N$ 标示单位 $1, \ldots, i, \ldots, N$ 包含了一个很大的，比如几千个兴趣领域，比如不同种族不同主要职业群体的人的家庭他们的主要收入成员分布在不同的县，不同的州，比如美国为了某些总体的一般目的，一个样本 $s$ 大小相同 $n$，也可能相当大，比如几千，可能是根据设计选择的 $p$ 承认 $\pi_i>0$． 然后是总数 $T_d=\sum_{U_d} Y_i$ 对于感兴趣的变量 $y$ 与某一特定领域的成员有关的 $U_d$ 大小 $N_d$ 感兴趣的可以用直接估计量来估计
$$
t_d=\left(\sum_{s_d} Y_i / \pi_i\right)
$$
或
$$
t_d^{\prime}=N_d\left(\sum_{s_d} Y_i / \pi_i\right) /\left(\sum_{s_d} 1 / \pi_i\right) .
$$
我们写 $s_d$ 对于样本的一部分 $s$ 这与 $U_d$，和 $n_d$ 的大小 $s_d, d=1, \ldots, D$，写作 $D$ 对于这样的域的总数 $U_d$ 是不相交的，与 $U$ 当所有的 $U_d$ ’’ $d=1, \ldots, D$． 我们认为 $D$ 是非常大的，所以即使是大的 $n=\sum_{d=1}^D n_d$的值 $n_d$ 的许多值 $d$ 结果是相当小的，很多甚至为零。的样本基 $t_d$ 或 $t_d^{\prime}$ 在实践中发生的是如此之小，以至于它们可能没有任何有用的目的，它们的大小和不稳定的方差估计，导致无关紧要的置信区间，在大多数情况下无法覆盖真正的域总数。类似的更尖锐的问题是域均值的估计 $\bar{T}_d=T_d / N_d$，将域大小写为 $N_d$，这通常是未知的。小域统计通常是指地理区域，因此被称为小区域或局部区域，因此小域统计需要一种特殊的参数估计方法。在本节中，我们将简要讨论涉及小区域或局部区域估计的几个问题。
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