Empirical and Hierarchical Bayesian Estimation in Finite Population Sampling under Structural Measurement Error Models

This paper considers simultaneous estimation of means from several strata. A model-based approach is taken, where the covariates in the superpopulation model are subject to measurement errors. Empirical Bayes (EB) and Hierarchical Bayes estimators of the strata means are developed and asymptotic optimality of EB estimators is proved. Their performances are examined and compared with that of the sample mean in a simulation study as well as in data analysis. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..