Parametric Empirical Bayes Point and Interval Estimation in Small Area Estimation from Complex Surveys

这项合作研究调查了与参数经验贝叶斯点和区间估计有关的各种问题，以及当数据来自复杂调查时参数经验贝叶斯小区域估计的不确定性的度量。此外，调查人员将进行参数经验贝叶斯分析的三个实际应用：(1)估计美国人口普查不足；(2)估计美国50个州和哥伦比亚特区四人家庭的收入中位数；(3)估计美国50个州和哥伦比亚特区的失业率。美国和海外的许多联邦机构越来越需要为人口的不同亚群提供可靠的小区域统计数据。通常的基于设计的调查估计值不适合于此目的，因为为大量人口设计的典型抽样调查包含的关于次级人口或感兴趣的小区域的信息很少。在抽样调查文献中，该问题通常被称为小面积(域)估计问题。利用复杂调查提供的信息，制定可靠的小区域统计数据和适当的不确定性措施是极其重要的。本研究将推进小区域估计方法的发展。

This collaborative research investigates various problems associated with parametric empirical Bayes point and interval estimation and measure of uncertainty of a parametric empirical Bayes small-area estimator when the data are obtained from a complex survey. In addition, the investigators will conduct three real world applications of parametric empirical Bayes analysis: (1) Estimation of U.S. Census undercount; (2) Estimation of the median income of four-person families for fifty U.S. States and the District of Columbia; and (3) Estimation of the unemployment rates for fifty U.S. states and the District of Columbia. There is a growing demand by many U.S. and overseas federal agencies to produce reliable small area statistics for various subgroups of a population. Usual design-based survey estimators are not suitable for this purpose since a typical sample survey being designed for a large population contains very little information regarding the sub-populations or small areas of interest. The problem is generally referred to as a small-area (domain) estimation problem in the sample survey literature. Development of reliable small-area statistics and suitable measures of uncertainty using information from complex surveys is extremely important. This research will advance small-area estimation methods.