Statistics Colloquium : Dr. Gauri Datta

Abstract: The Fay-Herriot model develops predictions of small area means of a continuous outcome of interest by modeling the mean function by a linear model based on suitable covariates. Model errors of the Fay-Herriot model that capture the difference between the true mean function and the linear regression are assumed to be independent with identical distribution across small areas. Often population means of contiguous small areas display a spatial pattern. If covariates used to model the mean function fail to capture the spatial pattern, the residual variation will be part of the random effects. Consequently, the independence and identical distribution assumption for the random effects will fail. To address such inadequacy, we consider spatial random-effect models using a Bayesian approach. We assess effectiveness of these spatial models based on a simulation study and a real application. We consider predictions of statewide four-person family median incomes for the U.S. states based on the 1990 Current Population Survey and the 1980 Census. We assess the accuracy of our predictions against the corresponding 1990 Census values, which are treated as "gold standards". In some applications presented below, many small areas are not included in the surveys, and, consequently, they have no sample data. For such areas, predictions of the Fay-Herriot model are only the synthetic regression means. Proposed spatial models generate better predictions of small area means of unsampled areas by modifying the usual synthetic regression means by using residuals from neighboring areas. Posterior distributions for the spatial models based on a useful class of improper prior densities on model parameters are shown to be proper under mild conditions. These results hold true even when many unsampled small areas have no direct estimates.