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.
