Empirical Bayes and Hierarchical Bayes Analysis of Small Area Means in Complex Surveys

大多数大规模全国调查的抽样设计和样本量通常是为了以所需的精确度对感兴趣的参数作出国家估计。经常需要为某些次国家区域(如州或县)提供同样精确度的类似估计。然而，与国家以下地区相关的小样本并不能产生可靠的估计。这类问题称为小面积估计问题。各联邦和地方政府机构需要可靠的小区域统计数据来制定政策和分配资金。经验贝叶斯(EB)和层次贝叶斯(HB)方法已被广泛用于产生小区域统计。这些方法使用显式的分层模型来借鉴相关资源的力量。本研究扩展了经验贝叶斯(EB)和层次贝叶斯(HB)方法，以解决小区域估计中的以下问题：(1)调查响应中的测量误差；(2)来自双框架抽样设计的小区域统计；(3)指数幂分布下的小样本均值估计。

The sampling design and sample size of most large scale national surveys are usually determined so as to produce a national estimate of a parameter of interest with a desired level of precision. Quite often there is a need to produce similar estimates with the same level of precision for certain subnational regions (such as states or counties). However, the small samples associated with subnational regions do not produce reliable estimates. Problems of this kind are known as small area estimation problems. Reliable small area statistics are needed by various federal and local government agencies for policy making and the allocation of funds. The empirical Bayes (EB) and hierarchical Bayes (HB) methods have been widely used to produce small area statistics. These methods use explicit hierarchical models to borrow strength from related resources. This research extends the empirical Bayes (EB) and hierarchical Bayes (HB) methods to address the following issues in small area estimation: (1) Measurement errors in survey responses; (2) Small area statistics from a dual-frame sampling design; and (3) Estimation of small sample means under exponential power distributions.