Empirical and Hierarchical Bayes Methods in Small Area Estimation Problems

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In large scale sample surveys, estimates of a variety of characteristics are frequently given for large populations. Similar estimates for smaller domains or areas also are required. Recently, considerable attention has been given to improve procedures related to small area estimation problems. The traditional sample survey estimators which use information from a given small area often yield large standard errors because of small sample size in the area. Reliable small area statistics are needed by many federal agencies for regional planning and allocating government resources. Among these are the Bureau of Labor Statistics, which is interested in providing estimates of the unemployment rate not only for the nation but also for the states and the Census Bureau which inevitably misses people and must face the problem of adjusting spatially for the undercounts. The investigator spent the last academic year at the Bureau of Labor Statistics and the Census Bureau as a Senior Research Fellow under the American Statistical Association/ National Science Foundation Fellowship Program. The proposed research is a continuation of his work at these agencies aimed at developing reliable small area statistics. Attention is focussed on various multivariate and time series models to combine information from related sources. The plan is to develop different empirical and hierarchical Bayes procedures. To determine measures of accuracy of the empirical Bayes estimators, second order approximations will be sought to the mean squared errors of the estimators. This will require the extension of the existing methodology to multivariate and time series modelling and also to the situation when the prior parameters are estimated by the method of maximum likelihood or restricted maximum likelihood. It is anticipated that the posterior mean and the posterior variance in a hierarchical Bayes analysis will involve multi-dimensional integrals. Different sampling-based methods to evaluate the integrals will be investigated. In this context the modification and approximation of the Gibbs sampling method will be considered. The principal investigator has a solid research record in small area estimation and is well equipped by experience and by his collaborative ties with leading statisticians in the field to conduct the proposed research. His successes in this project will readily find applications in the particular areas of government with which he is familiar and other important arenas as well.