Robust Empirical Bayes Estimation of Means from Stratified Samples

Abstract

Abstract This article considers simultaneous estimation of means from several strata, where each stratum contains a finite number of elements. For example, quite often estimates of annual incomes, unemployment rates, and so forth must be made simultaneously for many areas. Our results find application in small area estimation where very few samples are available from an individual area, and an estimate of a certain area mean or simultaneous estimates of several area means can be improved by incorporating information from similar neighboring areas. Ghosh and Meeden (1986) considered empirical Bayes estimation of the finite population mean assuming a normal superpopulation model. Their estimators generalize automatically when one estimates a vector of stratum means. This article relaxes the normality assumption and assumes instead that the posterior expectation of any stratum mean is a linear function of the sample observations. This is the so-called “posterior linearity” property as described in Ericson (1...