P. Lahiri, et Mukherjee, Kanchan, On the Design-Consistency Property of Hierarchical Bayes Estimators in Finite Population Sampling, Annals of statistics , 35(2), 2007, pp. 724-737
We obtain a limit of a hierarchical Bayes estimator of a finite population mean when the sample size is large. The limit is in the sense of ordinary calculus, where the sample observations are treated as fixed quantities. Our result suggests a simple way to correct the hierarchical Bayes estimator to achieve design-consistency, a well-known property in the traditional randomization approach to finite population sampling. We also suggest three different measures of uncertainty of our proposed estimator.