两阶段抽样设计的推论及其在城市政策研究中的应用
Inference for two-stage sampling designs with application to a panel for urban policy
摘要：
住户和健康调查通常采用两阶段抽样设计。为了产生具有各种置信区间的可靠估计量，需要Horvitz-Thompson估计量的一些基本统计性质，如一致性和渐近正态性，以及各种方差估计量的一致性。这些性质主要是研究单阶段抽样设计。在这项工作中，我们证明了一致性的Horvitz-Thompson估计和相关的方差估计的一般类的两阶段抽样设计，在温和的假设。我们还研究了第一阶段采用大熵抽样设计的两阶段抽样，并通过耦合论证证明了Horvitz-Thompson估计量是渐近正态分布的。当第一级抽样比可忽略时，本文提出了简化的方差估计，它不需要估计一级单元内的方差，并证明了它们是相容的。一个应用程序的城市政策，这是这项工作的最初动机小组，也提出。
英文摘要：
Two-stage sampling designs are commonly used for household and health surveys. To produce reliable estimators with assorted confidence intervals, some basic statistical properties like consistency and asymptotic normality of the Horvitz-Thompson estimator are desirable, along with the consistency of assorted variance estimators. These properties have been mainly studied for single-stage sampling designs. In this work, we prove the consistency of the Horvitz-Thompson estimator and of associated variance estimators for a general class of two-stage sampling designs, under mild assumptions. We also study two-stage sampling with a large entropy sampling design at the first stage, and prove that the Horvitz-Thompson estimator is asymptotically normally distributed through a coupling argument. When the first-stage sampling fraction is negligible, simplified variance estimators which do not require estimating the variance within the Primary Sampling Units are proposed, and shown to be consistent. An application to a panel for urban policy, which is the initial motivation for this work, is also presented.
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