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

本合作研究探讨了从复杂调查中获得数据时，与参数经验贝叶斯点和区间估计以及参数经验贝叶斯小面积估计器的不确定性测量相关的各种问题。此外，研究人员将进行参数实证贝叶斯分析的三个实际应用：(1)估计美国人口普查漏报；(2)美国50个州和哥伦比亚特区四口之家的收入中位数估算；(3)估计美国50个州和哥伦比亚特区的失业率。许多美国和海外联邦机构越来越需要为人口的各个亚群体提供可靠的小区域统计数据。通常的基于设计的调查估计不适合这个目的，因为为大量人口设计的典型抽样调查包含的关于子人口或小兴趣区域的信息非常少。在样本调查文献中，这个问题通常被称为小区域（域）估计问题。利用来自复杂调查的信息制定可靠的小地区统计数据和适当的不确定性措施是极其重要的。本研究将推动小面积估算方法的发展。

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.