This research focuses on the development of parametric and semiparametric hierarchical Bayesian methods for small area estimation. Direct survey estimates of local areas (such as a county, municipality, or census division) are usually accompanied by large standard errors and coefficients of variation due to smallness of samples sizes in these areas. The prime reason for this is that the original survey was targeted to achieve accuracy at a much higher level of aggregation than that for local areas. This makes it a necessity to `borrow strength` or use information from similar local areas. Hierarchical and empirical Bayes methods are particularly well-suited to meet this need. Much of the Bayesian literature, however, is restricted to normal theory hierarchical and empirical Bayes estimation of small area means and other characteristics of interest, and that too has almost exclusively been parametric, assuming normality of the local area effects. One of the major components of this research is the development of semiparametric hierarchical Bayesian methods that avoid assuming normality of the local area effects. These methods are applicable to both linear and generalized linear models. Specific applications of these methods will involve estimation of median income of four-person families, estimation of income and poverty for small places like counties, subcounties, census tracts, etc. The methodology is applicable to other problems and can be used for the analysis of both discrete and continuous data. The second aspect of this research is small area estimation for more complex surveys, such as stratified two-stage sampling, where the local areas consist of primary units which cut across the stratum boundaries. Both parametric and semiparametric hierarchical Bayesian methods will be pursued here and the results will be compared.
