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Neyman-type sample allocation for domains-efficient estimation in multistage sampling
AStA Advances in Statistical Analysis ( IF 1.4 ) Pub Date : 2018-09-19 , DOI: 10.1007/s10182-018-00340-2
M. G. M. Khan , Jacek Wesołowski

We consider a problem of allocation of a sample in two- and three-stage sampling. We seek allocation which is both multi-domain and population efficient. Choudhry et al. (Survey Methods 38(1):23–29, 2012) recently considered such problem for one-stage stratified simple random sampling without replacement in domains. Their approach was through minimization of the sample size under constraints on relative variances in all domains and on the overall relative variance. To attain this goal, they used nonlinear programming. Alternatively, we minimize here the relative variances in all domains (controlling them through given priority weights) as well as the overall relative variance under constraints imposed on total (expected) cost. We consider several two- and three-stage sampling schemes. Our aim is to shed some light on the analytic structure of solutions rather than in deriving a purely numerical tool for sample allocation. To this end, we develop the eigenproblem methodology introduced in optimal allocation problems in Niemiro and Wesołowski (Appl Math 28:73–82, 2001) and recently updated in Wesołowski and Wieczorkowski (Commun Stat Theory Methods 46(5):2212–2231, 2017) by taking under account several new sampling schemes and, more importantly, by the (single) total expected variable cost constraint. Such approach allows for solutions which are direct generalization of the Neyman-type allocation. The structure of the solution is deciphered from the explicit allocation formulas given in terms of an eigenvector \({\underline{v}}^*\) of a population-based matrix \(\mathbf{D}\). The solution we provide can be viewed as a multi-domain version of the Neyman-type allocation in multistage stratified SRSWOR schemes.

中文翻译:

Neyman型样本分配用于多阶段采样中的领域有效估计

我们考虑在两阶段和三阶段抽样中分配样本的问题。我们寻求分配既有效又能有效分配人口的分配。Choudhry等。(Survey Methods 38(1):23–29,2012)最近考虑了在没有域替换的情况下进行一阶段分层简单随机抽样的问题。他们的方法是在所有领域的相对方差和整体相对方差的约束下,通过使样本规模最小化。为了实现这一目标,他们使用了非线性编程。或者,我们在这里最小化所有域中的相对方差(通过给定的优先权重进行控制),以及在总(预期)成本所施加的约束下的整体相对方差。我们考虑几种两阶段和三阶段采样方案。我们的目的是阐明解决方案的分析结构,而不是得出用于样本分配的纯数值工具。为此,我们开发了特征问题方法,该方法在Niemiro和Wesołowski(应用数学28:73-82,2001)中引入了最优分配问题,并在Wesołowski和Wieczorkowski(公共统计理论方法46(5):2212-2231, (2017年),考虑了几个新的抽样方案,更重要的是考虑了(单个)总预期可变成本约束。这种方法允许直接对奈曼类型分配进行概括的解决方案。解决方案的结构是根据以特征向量给出的显式分配公式破译的 我们开发了特征问题方法,该方法在Niemiro和Wesołowski(应用数学28:73–82,2001)中引入了最优分配问题,最近在Wesołowski和Wieczorkowski(公共统计理论方法46(5):2212–2231,2017)中进行了更新。考虑了几个新的抽样方案,更重要的是,受到(单个)总预期可变成本约束。这种方法允许直接对奈曼类型分配进行概括的解决方案。解决方案的结构是根据以特征向量给出的显式分配公式破译的 我们开发了特征问题方法,该方法在Niemiro和Wesołowski(应用数学28:73–82,2001)中引入了最优分配问题,最近在Wesołowski和Wieczorkowski(公共统计理论方法46(5):2212–2231,2017)中进行了更新。考虑了几个新的抽样方案,更重要的是,受到(单个)总预期可变成本约束。这种方法允许直接对奈曼类型分配进行概括的解决方案。解决方案的结构是根据以特征向量给出的显式分配公式破译的 更重要的是,受(单个)总预期可变成本约束。这种方法允许直接对奈曼类型分配进行概括的解决方案。解决方案的结构是根据以特征向量给出的显式分配公式破译的 更重要的是,受(单个)总预期可变成本约束。这种方法允许直接对奈曼类型分配进行概括的解决方案。解决方案的结构是根据以特征向量给出的显式分配公式破译的基于人口的矩阵\(\ mathbf {D} \)的\({\下划线{v}} ^ * \)。我们提供的解决方案可以看作是多阶段分层SRSWOR方案中Neyman类型分配的多域版本。
更新日期:2018-09-19
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