Collaborative Research: Empirical and Hierarchical Bayesian Methods with Applications to Small Area Estimation

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The project will introduce some new empirical and hierarchical Bayesian (EB and HB) methodology which can be used in a wide range of problems in demography, sociology, business, insurance, economics, and surveys. In particular, the methods are expected to be readily applicable to certain small area estimation problems involving both discrete and continuous data. The two major motivating examples for this research are estimation of the proportion of uninsured for minority subpopulations and neighborhood level estimation of the proportion of African-American females suffering from clinical depression. The first topic is of immense relevance to many Federal Agencies such as the Center for Disease Control/National Center for Health Statistics and the United States Bureau of the Census. The second is of direct relevance to researchers engaged in Family and Community Health Study. The project is expected to develop a general class of EB confidence intervals not only for continuous data, but also for discrete data, such as binary and count data. The research will also address robust HB and EB estimation. The general methodology will have direct application to the specific examples mentioned earlier and beyond.The broader impact of the proposed research is enormous. The development of simple and easy to use EB confidence intervals will be an advancement not only for the small area literature, but also for a wide range of problems in demography, sociology, business, economics and insurance where EB methods are routinely used. The simplicity and data-adaptability of these intervals will make them readily usable not only for binary and count data, but also for skewed continuous data fitted by the exponential and gamma distributions. Also, the construction of robust HB and EB estimators will provide a strong theoretically viable method for simultaneous estimation problems, once again routinely faced in diverse research areas. In addition, the proposed research will contribute towards research-based training of graduate students, involve participation of under-represented groups and foster interagency and interdisciplinary collaboration. The new research results also will be incorporated in graduate courses on survey sampling. This award was supported as part of the fiscal year 2006 Mathematical Sciences priority area special competition on Mathematical Social and Behavioral Sciences (MSBS).