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|Subsampling of Second-Stage Units to Simplify Variance Estimation
SRINATH and HIDIROGLOU (1980) contrived the following device to bypass the requirement of estimating $V_L\left(T_i\right)$. They consider choosing the fsus by SRSWOR scheme, choosing from each sampled fsu $i$ in the sample $s$ again an SRSWOR $s_i$, in independent manners cluster-wise of size $m_i$ from $M_i$ ssus in it, and using
$$
e=\frac{N}{n} \sum_{i \in s} M_i \bar{y}_i
$$
as an estimator for $Y$. Here $\bar{y}_i$ is the mean of the $y$ values of the ssus in $s_i$ for $i \in s$. Then they recommend taking a subsample $s_i^{\prime}$ of size $m_i^{\prime}$ out of $s_i$ again by SRSWOR method, getting $\bar{y}_i^{\prime}$ as the mean of $y$ based on the ssus in $s_i^{\prime}$. They show that an unbiased estimator for $V(e)$ is available exclusively in terms of $\bar{y}_i^{\prime}$ for $i \in s$ although not in terms of $\bar{y}_i$ as, ideally, one would like to have.
ARNAB (1988) argues that restriction to SRSWOR is neither necessary nor desirable and discarding the ssus in $s_i$ or $s_i^{\prime}$ is neither desirable nor necessary, and gives further generalizations of this basic idea of SRINATH and HIDIROGLOU (1980). Following DES RAJ’s (1968) general strategy, he suggests starting with the estimator
$$
e_D=\sum_s b_{s i} I_{s i} T_i
$$
with
$$
\begin{aligned}
V\left(e_D\right) & =\sum Y_i^2\left(\alpha_i-1\right)+\sum_{i \neq j} Y_i Y_j\left(\alpha_{i j}-1\right)+\sum \alpha_i \sigma_i^2 \
V_L\left(T_i\right) & =\sigma_i^2
\end{aligned}
$$
统计代写|抽样调查作业代写sampling theory of survey代考|Estimation of Y
We have so far restricted ourselves to only unbiased estimators of $Y$. But suppose we want to estimate
$$
\bar{Y}=\sum_1^N Y_i / \sum_1^N M_i
$$
where $\sum_1^N M_i$ may also be unknown like $Y=\sum_1^N Y_i$ and we may know or ascertain only the values of $M_i$ for the clusters actually selected. In that case, an unbiased estimator is unlikely to be available for $\bar{Y}$. Rather, a biased ratio estimator $t_R=\Sigma_s Y_i / \Sigma_s M_i$ may be based on an SRSWOR $s$ of selected clusters if $Y_i$ ‘s are ascertainable. If not, one may employ
$$
e_R=\frac{\sum_s T_i}{\sum_s M_i},
$$
a biased estimator for $\bar{Y}$, using $T_i$ ‘s as unbiased estimators for $Y_i$ based on samples taken at later stages of sampling from the fsu $i$ such that $E_L\left(T_i\right)=Y_i$ with $V_L\left(T_i\right)$ equal to $V_{s i}$ or $\sigma_i^2$ admitting respectively unbiased estimators $\hat{V}{s i}$ or $\hat{\sigma}_i^2$ such that $E_L\left(\hat{V}{s i}\right)=V_{s i}$ or $E_L\left(\hat{\sigma}_i^2\right)=\sigma_i^2$.
In general, following RAO and VIJAYAN (1977) and RAO (1979), let us start with
$$
t=\sum_s b_{s i} I_{s i} Y_i
$$
not necessarily unbiased for $Y$ such that
$$
M=E_p(t-Y)^2=\sum \sum Y_i Y_j d_{i j}
$$
with
$$
E_p\left(b_{s i} I_{s i}-1\right)\left(b_{s j} I_{s j}-1\right)=d_{i j} .
$$
Let us assume that there exist $W_i \neq 0$ such that if $Z_i=$ $Y_i / W_i=c$ (a non-zero constant) for all $i$, then $M$ equals zero. In that case, from chapter 2 we know that we may write
$$
\begin{aligned}
M & =-\sum_{i<j} d_{i j} W_i W_j\left(Z_i-Z_j\right)^2 \
& =-\sum_{i<j} d_{i j} W_i W_j\left(\frac{Y_i}{W_i}-\frac{Y_j}{W_j}\right)^2 .
\end{aligned}
$$
抽样调查代考
统计代写|抽样调查作业代写sampling theory of survey代考|Subsampling of Second-Stage Units to Simplify Variance Estimation
SRINATH和HIDIROGLOU(1980)设计了以下装置来绕过估算$V_L\left(T_i\right)$的要求。他们考虑通过SRSWOR方案选择fsu，从样本中每个抽样的fsu $i$$s$中再次选择SRSWOR $s_i$，以独立的方式从$M_i$中的ssu中选择大小为$m_i$的集群，并使用
$$
e=\frac{N}{n} \sum_{i \in s} M_i \bar{y}_i
$$
作为$Y$的估计值。这里$\bar{y}_i$是$i \in s$中$s_i$中ssus的$y$值的平均值。然后，他们建议再次用SRSWOR方法从$s_i$中取出大小为$m_i^{\prime}$的子样本$s_i^{\prime}$，根据$s_i^{\prime}$中的ssus得到$\bar{y}_i^{\prime}$作为$y$的平均值。它们表明，$V(e)$的无偏估计量只能在$i \in s$的$\bar{y}_i^{\prime}$项下可用，尽管在理想情况下不能在$\bar{y}_i$项下可用。
ARNAB(1988)认为限制SRSWOR既不必要也不可取，丢弃$s_i$或$s_i^{\prime}$中的ssus既不可取也不必要，并进一步概括了SRINATH和HIDIROGLOU(1980)的基本思想。根据DES RAJ(1968)的一般策略，他建议从估计器开始
$$
e_D=\sum_s b_{s i} I_{s i} T_i
$$
有
$$
\begin{aligned}
V\left(e_D\right) & =\sum Y_i^2\left(\alpha_i-1\right)+\sum_{i \neq j} Y_i Y_j\left(\alpha_{i j}-1\right)+\sum \alpha_i \sigma_i^2 \
V_L\left(T_i\right) & =\sigma_i^2
\end{aligned}
$$
统计代写|抽样调查作业代写sampling theory of survey代考|Estimation of Y
到目前为止，我们仅限于$Y$的无偏估计量。但是假设我们想要估计
$$
\bar{Y}=\sum_1^N Y_i / \sum_1^N M_i
$$
其中$\sum_1^N M_i$也可能像$Y=\sum_1^N Y_i$一样是未知的，我们可能只知道或确定实际选择的集群的$M_i$的值。在这种情况下，无偏估计量不太可能用于$\bar{Y}$。相反，如果$Y_i$是可确定的，则偏比值估计器$t_R=\Sigma_s Y_i / \Sigma_s M_i$可以基于所选簇的SRSWOR $s$。如果没有，可以雇佣
$$
e_R=\frac{\sum_s T_i}{\sum_s M_i},
$$
$\bar{Y}$的有偏估计，使用$T_i$作为$Y_i$的无偏估计，基于从fsu $i$采样的后期阶段的样本，使得$E_L\left(T_i\right)=Y_i$与$V_L\left(T_i\right)$等于$V_{s i}$或$\sigma_i^2$分别承认无偏估计$\hat{V}{s i}$或$\hat{\sigma}i^2$，使得$E_L\left(\hat{V}{s i}\right)=V{s i}$或$E_L\left(\hat{\sigma}_i^2\right)=\sigma_i^2$。
总的来说，继RAO和VIJAYAN(1977)和RAO(1979)之后，让我们从
$$
t=\sum_s b_{s i} I_{s i} Y_i
$$
对于$Y$来说不一定是公正的
$$
M=E_p(t-Y)^2=\sum \sum Y_i Y_j d_{i j}
$$
有
$$
E_p\left(b_{s i} I_{s i}-1\right)\left(b_{s j} I_{s j}-1\right)=d_{i j} .
$$
让我们假设存在$W_i \neq 0$，如果$Z_i=$$Y_i / W_i=c$(一个非零常数)对于所有$i$，那么$M$等于零。在这种情况下，从第二章我们知道我们可以写
$$
\begin{aligned}
M & =-\sum_{i<j} d_{i j} W_i W_j\left(Z_i-Z_j\right)^2 \
& =-\sum_{i<j} d_{i j} W_i W_j\left(\frac{Y_i}{W_i}-\frac{Y_j}{W_j}\right)^2 .
\end{aligned}
$$
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