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。

couryes-lab™ 为您的留学生涯保驾护航 在代写抽样调查sampling theory of survey方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写抽样调查sampling theory of survey方面经验极为丰富，各种代写抽样调查sampling theory of survey相关的作业也就用不着说。

我们提供的抽样调查sampling theory of survey及其相关学科的代写，服务范围广, 其中包括但不限于:

统计代写|抽样调查作业代写sampling theory of survey代考|Synthetic Estimators

Since $n_{d g}$ and $n_{d g h}$ ‘s are very small, if we may believe that the $g$ groups have been so effectively formed that in respect of the characteristics of interest $y$ there is homogeneity within each separate group across the domains, then the following broadbased estimators for $T_d$ may be useful
$$
\begin{aligned}
t_{c s d} & =\sum_g N_{d_g}\left(\Sigma_{s . g} Y_k / \pi_k\right) /\left(\Sigma_{s, g} 1 / \pi_k\right) \
t_{c s c d} & =\sum_g\left(\Sigma_{H_d} N_{d g h}\right)\left(\Sigma_{H_d} \Sigma_{s, g h} Y_k / \pi_k\right) /\left(\Sigma_{H_d} \Sigma_{s, g h} 1 / \pi_k\right) \
t_{c s s d}^{\prime} & =\sum_g \Sigma_{H_d} N_{d g h}\left(\Sigma_{s, g h} Y_k / \pi_k\right) /\left(\Sigma_{s, g h} 1 / \pi_k\right)
\end{aligned}
$$
called the count-synthetic estimators for unstratified, stratified-combined, and stratified-separate sampling, respectively. The corresponding ratio-synthetic estimators for unstratified and stratified sampling are:
$$
\begin{aligned}
t_{R s d} & =\sum_g X_{d g}\left(\Sigma_{s, g} Y_k / \pi_k\right) /\left(\Sigma_{s, g} X_k / \pi_k\right) \
t_{R s c d} & =\sum_g\left(\Sigma_{H_d} X_{d g h}\right) \frac{\left(\Sigma_{H_d} \Sigma_{s, g h} Y_k / \pi_k\right)}{\left(\Sigma_{H_d} \Sigma_{s, g h} X_k / \pi_k\right)} \
t_{R_{s e d}} & =\sum_g \Sigma_{H_d} X_{d g h}\left(\Sigma_{s, g h} Y_k / \pi_k\right) /\left(\Sigma_{s, g h} X_k / \pi_k\right) .
\end{aligned}
$$
For SRSWOR from $U$ and independent SRSWORs from $U . . h$, we have the six simpler synthetic estimators
$$
\begin{aligned}
t_1 & =\sum_g N_{d g} \bar{y}{g g} \ t_2 & =\sum_g X{d g} \frac{\bar{y}{g g}}{\bar{x}_g}, \ t_3 & =\sum_g \Sigma{H_d} N_{d g h}\left(\Sigma_{H_d} \frac{N . . h}{n . . h} n_{g h} \bar{y}{g h}\right) /\left(\Sigma{H_d} \frac{N . . h}{n . . h} n_{g h}\right) \
t_4 & =\sum_g \Sigma_{H_d} N_{d g h} \bar{y}{g h} \ t_5 & =\sum_g \Sigma{H_d} X_{d g h} \frac{\left(\Sigma_{H_d} \frac{N . h}{n . h} n_{g h} \bar{y}{g h}\right)}{\left(\Sigma{H_d} \frac{N . h}{n . h} n_{g h} \bar{x}{g h}\right)} \ t_6 & =\sum_g \Sigma{H_d} X_{d g h} \frac{\bar{y}{g h}}{\bar{x}{g h}} .
\end{aligned}
$$

统计代写|抽样调查作业代写sampling theory of survey代考|Model-Based Estimation

An alternative procedure of small area estimation involving a technique of borrowing strength is the following. Suppose $T_d, d=1, \ldots, D$ are the true values for large number, $D$, of domains of interest and, employing suitable sampling schemes, estimates $t_d$ for $d \in s_0$ are obtained, where $s_0$ is a subset of $m$ domains. Now, suppose auxiliary characters $x_j, j=1, \ldots, K$ are available with known values $X_{j d}, d=1, \ldots, D$. Then, postulating a linear multiple regression
$$
T_d=\beta_0+\beta_1 X_{1 d}+\ldots+\beta_K X_{K d}+\epsilon_d ; d=1, \ldots, m
$$
one may write for $d \epsilon s_0$
$$
t_d=\beta_0+\beta_1 X_{1 d}+\ldots+\beta_K X_{K d}+e_d+\epsilon_d
$$
writing $e_d=t_d-T_d$, the error in estimating $T_d$ by $t_d$. Now applying the principle of least squares utilizing the sampled values, one may get estimates $\widehat{\beta}j$ for $j=0,1, \ldots, K$ based on $\left(t_d, X{j d}\right)$ for $d \epsilon s_0$ and $j=1, \ldots, K$, assuming $m>K+1$. Then, we may take $\sum_0^K \widehat{\beta}j X{j d}=\widehat{T}_d$ as estimates for $T_d$ not only for $d \epsilon s_0$ but also for the remaining domains $d \notin s_0$.

This method has been found by ERICKSEN (1974) to work well in many situations of estimating current population figures in large numbers of U.S. counties and in correcting census undercounts. An obvious step forward is to combine the estimators $t_d$ with $\widehat{T}_d$ for $d=1, \ldots, m$ to derive estimators that should outperform both $t_d$ and $\widehat{T}_d, d=1, \ldots, m$. Postulating that $e_d$ ‘s and $\epsilon_d$ ‘s are mutually independent and separately iid random variates respectively distributed as $N\left(0, \sigma^2\right)$ and $N\left(0, \tau^2\right)$, following GHOSH and MEEDEN (1986) one may derive weighted estimators
$$
t_d^*=\frac{\tau^2}{\sigma^2+\tau^2} t_d+\frac{\sigma^2}{\sigma^2+\tau^2} \widehat{T}_d, d=1, \ldots, m
$$
provided $\sigma$ and $\tau$ are known. If they are unknown, they are to be replaced by suitable estimators. Thus, here we may use JAMES-STEIN or empirical Bayes estimators of the form
$$
\widehat{t}_d=\widehat{W} t_d+(1-\widehat{W}) \widehat{T}_d
$$
with $0<\widehat{W}<1$, such that according as $t_d\left(\widehat{T}_d\right)$ is more accurate for $T_d$, the weight $\widehat{W}$ goes closer to $1(0)$. These procedures we have explained and illustrated in section 4.2. PRASAD (1988) is an important reference.

抽样调查代考

统计代写|抽样调查作业代写sampling theory of survey代考|Synthetic Estimators

由于$n_{d g}$和$n_{d g h}$非常小，如果我们可以相信$g$组已经如此有效地形成，就感兴趣的特征而言$y$在跨域的每个单独组中存在同质性，那么下面的$T_d$的宽基估计可能是有用的
$$
\begin{aligned}
t_{c s d} & =\sum_g N_{d_g}\left(\Sigma_{s . g} Y_k / \pi_k\right) /\left(\Sigma_{s, g} 1 / \pi_k\right) \
t_{c s c d} & =\sum_g\left(\Sigma_{H_d} N_{d g h}\right)\left(\Sigma_{H_d} \Sigma_{s, g h} Y_k / \pi_k\right) /\left(\Sigma_{H_d} \Sigma_{s, g h} 1 / \pi_k\right) \
t_{c s s d}^{\prime} & =\sum_g \Sigma_{H_d} N_{d g h}\left(\Sigma_{s, g h} Y_k / \pi_k\right) /\left(\Sigma_{s, g h} 1 / \pi_k\right)
\end{aligned}
$$
分别称为非分层、分层组合和分层分离抽样的计数合成估计器。非分层和分层抽样对应的比值综合估计量为:
$$
\begin{aligned}
t_{R s d} & =\sum_g X_{d g}\left(\Sigma_{s, g} Y_k / \pi_k\right) /\left(\Sigma_{s, g} X_k / \pi_k\right) \
t_{R s c d} & =\sum_g\left(\Sigma_{H_d} X_{d g h}\right) \frac{\left(\Sigma_{H_d} \Sigma_{s, g h} Y_k / \pi_k\right)}{\left(\Sigma_{H_d} \Sigma_{s, g h} X_k / \pi_k\right)} \
t_{R_{s e d}} & =\sum_g \Sigma_{H_d} X_{d g h}\left(\Sigma_{s, g h} Y_k / \pi_k\right) /\left(\Sigma_{s, g h} X_k / \pi_k\right) .
\end{aligned}
$$
对于来自$U$的SRSWOR和来自$U . . h$的独立SRSWOR，我们有六个更简单的综合估计器
$$
\begin{aligned}
t_1 & =\sum_g N_{d g} \bar{y}{g g} \ t_2 & =\sum_g X{d g} \frac{\bar{y}{g g}}{\bar{x}g}, \ t_3 & =\sum_g \Sigma{H_d} N{d g h}\left(\Sigma_{H_d} \frac{N . . h}{n . . h} n_{g h} \bar{y}{g h}\right) /\left(\Sigma{H_d} \frac{N . . h}{n . . h} n_{g h}\right) \
t_4 & =\sum_g \Sigma_{H_d} N_{d g h} \bar{y}{g h} \ t_5 & =\sum_g \Sigma{H_d} X_{d g h} \frac{\left(\Sigma_{H_d} \frac{N . h}{n . h} n_{g h} \bar{y}{g h}\right)}{\left(\Sigma{H_d} \frac{N . h}{n . h} n_{g h} \bar{x}{g h}\right)} \ t_6 & =\sum_g \Sigma{H_d} X_{d g h} \frac{\bar{y}{g h}}{\bar{x}{g h}} .
\end{aligned}
$$

统计代写|抽样调查作业代写sampling theory of survey代考|Model-Based Estimation

下面是另一种涉及借用强度技术的小面积估计程序。假设$T_d, d=1, \ldots, D$是大量感兴趣的域$D$的真实值，并且采用合适的抽样方案，得到$d \in s_0$的估计值$t_d$，其中$s_0$是$m$域的子集。现在，假设辅助字符$x_j, j=1, \ldots, K$具有已知值$X_{j d}, d=1, \ldots, D$。然后，假设一个线性多元回归
$$
T_d=\beta_0+\beta_1 X_{1 d}+\ldots+\beta_K X_{K d}+\epsilon_d ; d=1, \ldots, m
$$
可以为$d \epsilon s_0$写信
$$
t_d=\beta_0+\beta_1 X_{1 d}+\ldots+\beta_K X_{K d}+e_d+\epsilon_d
$$
写$e_d=t_d-T_d$，用$t_d$估计$T_d$的误差。现在利用采样值应用最小二乘原理，可以根据$d \epsilon s_0$和$j=1, \ldots, K$的$\left(t_d, X{j d}\right)$得到$j=0,1, \ldots, K$的估计值$\widehat{\beta}j$，假设$m>K+1$。然后，我们可以将$\sum_0^K \widehat{\beta}j X{j d}=\widehat{T}_d$作为$T_d$的估计值，不仅对于$d \epsilon s_0$，而且对于其余的域$d \notin s_0$。

ERICKSEN(1974)发现，这种方法在估计大量美国县的当前人口数据和纠正人口普查不足的许多情况下都很有效。一个明显的进步是将$d=1, \ldots, m$的估计器$t_d$与$\widehat{T}_d$结合起来，以推导出性能应该优于$t_d$和$\widehat{T}_d, d=1, \ldots, m$的估计器。假设$e_d$ ‘s和$\epsilon_d$ ‘s是相互独立的独立随机变量，分别分布为$N\left(0, \sigma^2\right)$和$N\left(0, \tau^2\right)$，根据GHOSH和MEEDEN(1986)，可以得到加权估计量
$$
t_d^*=\frac{\tau^2}{\sigma^2+\tau^2} t_d+\frac{\sigma^2}{\sigma^2+\tau^2} \widehat{T}_d, d=1, \ldots, m
$$
假设已知$\sigma$和$\tau$。如果它们是未知的，它们将被合适的估计器所取代。因此，这里我们可以使用JAMES-STEIN或经验贝叶斯估计的形式
$$
\widehat{t}_d=\widehat{W} t_d+(1-\widehat{W}) \widehat{T}_d
$$
对于$0<\widehat{W}<1$，根据$t_d\left(\widehat{T}_d\right)$对$T_d$更准确，权重$\widehat{W}$更接近$1(0)$。我们已经在4.2节中解释和说明了这些过程。PRASAD(1988)是一个重要的参考。

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