COUPLING METHODS FOR MULTISTAGE SAMPLING
COUPLING METHODS FOR MULTISTAGE SAMPLING
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DOI：
10.1214/15-aos1348
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发表时间：
2015-12-01
影响因子：
4.5
通讯作者：
Chauvet, Guillaume
中科院分区：
文献类型：
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作者：
Chauvet, Guillaume
在没有抽样框架或人口分布较广的情况下，多阶段抽样通常用于住户调查。多阶段抽样通常在最终单位的选择中引入复杂的依赖关系，这使得渐近结果很难证明。在这项工作中，我们考虑在第一阶段采用简单随机不替换抽样的多阶段抽样，并在后续阶段采用任意抽样设计。我们考虑耦合方法，将这种抽样设计与独立选择主要抽样单位的抽样设计联系起来。我们首先推广Magyar Tud引入的一种方法。Akad。马特·库塔托Kozl. 5(1960) 361-374]得到了多阶段抽样和第一阶段伯努利抽样的耦合，从而得到了Horvitz-Thompson估计量的中心极限定理。在此基础上，提出了一种多阶段抽样与简单随机的耦合方法。当第一阶段抽样分数趋于零时，用该方法证明了在第一阶段无替换抽样的简单随机的有替换自举的一致性，以及总函数的光滑自举方差估计的一致性。
Multistage sampling is commonly used for household surveys when there exists no sampling frame, or when the population is scattered over a wide area. Multistage sampling usually introduces a complex dependence in the selection of the final units, which makes asymptotic results quite difficult to prove. In this work, we consider multistage sampling with simple random without replacement sampling at the first stage, and with an arbitrary sampling design for further stages. We consider coupling methods to link this sampling design to sampling designs where the primary sampling units are selected independently. We first generalize a method introduced by [Magyar Tud. Akad. Mat. Kutato Int. Kozl. 5 (1960) 361-374] to get a coupling with multistage sampling and Bernoulli sampling at the first stage, which leads to a central limit theorem for the Horvitz-Thompson estimator. We then introduce a new coupling method with multistage sampling and simple random with replacement sampling at the first stage. When the first-stage sampling fraction tends to zero, this method is used to prove consistency of a with-replacement bootstrap for simple random without replacement sampling at the first stage, and consistency of bootstrap variance estimators for smooth functions of totals.