Empirical best prediction for small-area inference based on generalized linear mixed models

Abstract

The paper introduces a frequentist's alternative to the recently developed hierarchical Bayes methods for small-area estimation using generalized linear mixed models. Specifically, the best predictor and empirical best predictor (EBP) of small area specific random effect are derived in the context of a generalized linear mixed model. An approximation to the mean squared error (MSE) of the proposed EBP correct up to the order o( m −1) is obtained, where m denotes the number of small areas. As a special case, we consider a class of mixed logistic models, in which the asymptotic behavior of the relative savings loss demonstrates the superiority of the proposed EBP over the usual small area proportion.