Posted on Categories:Survey sampling, 抽样调查, 统计代写, 统计代考

统计代写|抽样调查代考Survey sampling代写|DOMAIN ESTIMATION

avatest™

avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

统计代写|抽样调查代考Survey sampling代写|DOMAIN ESTIMATION

Let $D$ be a domain of interest within a population $U=(1, \ldots$, $i, \ldots, N)$. Let $N_D$ be the unknown size of $D$. Let a sample $s$ of size $n$ be drawn from $U$ with a probability $p(s)$ according to a design $p$ admitting positive inclusion probabilities $\pi_i, \pi_{i j}$. Let for $i=1,2, \ldots, N$
\begin{aligned} & I_{D i}=1(0) \quad \text { if } \quad i \in D(i \notin D) \ & Y_{D i}=Y_i(0) \text { if } \quad i \in D(i \notin D) \text {. } \ & \end{aligned}
Then the unknown domain size, total, and mean are, respectively,
$$N_D=\sum_1^N I_{D i}, T_D=\sum_1^N Y_{D i} \quad \text { and } \quad \bar{T}D=\frac{T_D}{N_D}$$ In analogy to $\underline{Y}=\left(Y_1, \ldots, Y_i, \ldots, Y_N\right)^{\prime}$ we write $\underline{I}_D=\left(I{D 1}, \ldots\right.$, $\left.I_{D i}, \ldots, I_{D N}\right)^{\prime}$ and $\underline{Y}D=\left(Y{D 1}, \ldots, Y_{D i}, \ldots, Y_{D N}\right)^{\prime}$. Then, corresponding to any estimator $t=t(s, \underline{Y})=\hat{Y}$, for $Y=\Sigma_1^N Y_i$ we may immediately choose estimators for $N_D$ and $T_D$, respectively,
$$\widehat{N}_D=t\left(s, \underline{I}_D\right) \quad \text { and } \quad \widehat{T}_D=t\left(s, \underline{Y}_D\right) .$$
It may then be a natural step to take the estimator $\widehat{T}_D$ for $\bar{T}_D$ as
$$\widehat{T}_D=\frac{\widehat{T}_D}{\widehat{N}_D}$$

统计代写|抽样调查代考Survey sampling代写|POSTSTRATIFICATION

Suppose a finite population $U=(1, \ldots, i, \ldots, N)$ of $N$ units consists of $L$ post-strata of known sizes $N_h, h=1, \ldots, L$ but unknown compositions with respective post-strata totals $Y_h=$ $\sum_i^{N_h} Y_{h i}$ and means $\bar{Y}h=Y_h / N_h, h=1, \ldots, L$. Let a simple random sample $s$ of size $n$ have been drawn from $U$ yielding the sample configuration $\underline{n}=\left(n_1, \ldots, n_h, \ldots, n_L\right)$ where $n_h(\geq 0)$ is the number of units of $s$ coming from the $h$ th post-stratum, $h=1, \ldots, L, \sum{h=1}^L n_h=n$. In order to estimate $\bar{Y}=\Sigma W_h \bar{Y}h$, writing $W_h=\frac{N_h}{N}, h=1, \ldots, L$ we proceed as follows. Let $I_h=1(0)$ if $n_h>0\left(n_h=0\right)$. Then, $$E\left(I_h\right)=\operatorname{Prob}\left(I_h=1\right)=1-\left(\begin{array}{c} N-N_h \ n \end{array}\right) /\left(\begin{array}{c} N \ n \end{array}\right), h=1, \ldots, L .$$ For $\bar{Y}$ a reasonable estimator may be taken as $$t{p s t}=t_{p s t}(\underline{Y})=\frac{\sum W_h \bar{y}_h I_h / E\left(I_h\right)}{\sum W_h I_h / E\left(I_h\right)}$$
writing $\bar{y}_h$ as the mean of the $n_h$ units in the sample consisting of members of the $h$ th post-stratum, if $n_h>0$; if $n_h=0$, then $\bar{y}_h$ is taken as $\bar{Y}_h$. It follows that $x=\sum W_h \bar{y}_h I_h / E\left(I_h\right)$ is an unbiased estimator for $\bar{Y}$ and $b=\sum W_h I_h / E\left(I_h\right)$ an unbiased estimator for 1. Yet, instead of taking just a as an unbiased estimator for $\bar{Y}$, this biased estimator of the ratio form $\frac{x}{b}$ is proposed by DOSS, HARTLEY and SOMAYAJULU (1979) because it has the following linear invariance property not shared by itself:

Assume $Y_i=\alpha+\beta Z_i$; then $\bar{y}h=\alpha+\beta \bar{z}_h$ and $t{p s t}(\underline{Y})=$ $\alpha+\beta t_{p s t}(\underline{Z})$, with obvious notations. Further properties of $t_{p s t}$ have been investigated by Doss et al. (1979) but are too complicated to merit further discussion here.

抽样调查代写

统计代写|抽样调查代考Survey sampling代写|DOMAIN ESTIMATION

\begin{aligned} & I_{D i}=1(0) \quad \text { if } \quad i \in D(i \notin D) \ & Y_{D i}=Y_i(0) \text { if } \quad i \in D(i \notin D) \text {. } \ & \end{aligned}

$$N_D=\sum_1^N I_{D i}, T_D=\sum_1^N Y_{D i} \quad \text { and } \quad \bar{T}D=\frac{T_D}{N_D}$$与$\underline{Y}=\left(Y_1, \ldots, Y_i, \ldots, Y_N\right)^{\prime}$类似，我们写$\underline{I}D=\left(I{D 1}, \ldots\right.$, $\left.I{D i}, \ldots, I_{D N}\right)^{\prime}$和$\underline{Y}D=\left(Y{D 1}, \ldots, Y_{D i}, \ldots, Y_{D N}\right)^{\prime}$。然后，对应于任意估计量$t=t(s, \underline{Y})=\hat{Y}$，对于$Y=\Sigma_1^N Y_i$，我们可以立即分别选择$N_D$和$T_D$的估计量，
$$\widehat{N}_D=t\left(s, \underline{I}_D\right) \quad \text { and } \quad \widehat{T}_D=t\left(s, \underline{Y}_D\right) .$$

$$\widehat{T}_D=\frac{\widehat{T}_D}{\widehat{N}_D}$$

统计代写|抽样调查代考Survey sampling代写|POSTSTRATIFICATION

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。