Collaborative research: Topics in Small Area Estimation

术语“小区域”或“局部区域”通常指小的地理区域，如县、直辖市、人口普查区或学区。它也可以指社会人口统计领域，比如在一个大的地理区域内的一个特定的年龄、性别、种族群体。近年来，由于许多公共和私人机构需要可靠的小面积估算来制定有用的政策决策，小面积估算已成为一个越来越重要的话题。本项目旨在解决小面积估算的几个重要方面。在这种情况下需要解决的一个基本问题是，如何将调查权重（通常是总体中不同单位的选择概率的倒数）与模型结合起来，得出有意义的小区域估计值。虽然已经提出了许多专有的基于模型的小面积估计器，但设计辅助的基于模型的小面积估计器非常稀疏。我们的目标是为一类非常一般的分布获得这样的估计量。该方法将用于找出美国不同县贫困学龄儿童的比例和数量。对许多联邦机构来说，这是一个非常重要的问题，尤其是对人口普查局来说。这项研究的另一个方面是通过结合两个或多个旨在估计相同数量的兴趣的调查的结果来获得小面积估计。这一程序的典型应用包括结合基于当前人口调查（CPS）和人口普查局新引入的美国社区调查（ACS）的数据。美国人口普查计划在2010年取代十年一次的人口普查表格。最后，贝叶斯方法将用于在有限总体抽样中检测异常值，特别是在小面积估计的情况下。这项研究的更广泛的影响是，它旨在实现调查方法和调查实践之间的接口。举一个直接的例子，研究结果直接影响小区域收入和贫困估算，以及结合CPS和ACS两项调查的估算结果进行小区域估算。国家卫生统计中心（National Center for Health Statistics）的工作人员也应该对这些发现感兴趣，他们对估计不同种族的未参保人口比例、享受医疗补助的人口比例等感兴趣。

The term "small area" or "local area" usually refers to a small geographic area, such as a county, municipality, a census tract, or a school district. It can also refer to socio-demographic domains, such as a specific age-sex-race group within a large geographic area. Small area estimation has become a topic of growing importance in recent years because of the need for reliable small area estimates by many agencies, both public and private, for making useful policy decisions. This project is aimed at addressing several important aspects of small area estimation. One basic question to address in this context is how to use the survey weights (usually inverses of the selection probabilities of the different units in the population) in conjunction with models to arrive at meaningful small area estimators. While many exclusive model-based small area estimators have been proposed, design-assisted model-based small area estimators have been very sparse. The goal is to obtain such estimators for a very general class of distributions. The method will be used to find the proportion and the number of poor school-age children in different counties of the United States. This is a very important problem for many Federal agencies, especially for the Bureau of the Census. Another aspect of this research is to obtain small area estimates by combining results from two or more surveys designed to estimate the same quantity of interest. A typical application of this procedure consists of combining data based on the Current Population Survey (CPS) and the newly introduced American Community Survey (ACS) of the Bureau of the Census. The ACS is intended to replace the decennial census long form in the year 2010. Finally, Bayesian methods will be developed for detecting outliers in finite population sampling, especially in the context of small area estimation.The broader impact of this research is that it aims to achieve an interface between survey methodology and survey practice. As an immediate example, the research findings have direct bearing on small area income and poverty estimation as well as small area estimation by combining estimates from two surveys such as the CPS and the ACS. The findings also should be of interest to staff at the National Center for Health Statistics who are interested in estimating the proportion of uninsured people of different ethnicities, proportion of people under Medicaid, and so on.