Lahiri, P and Mukherjee, Kanchan (2007) On a design consistency property of hierarchical Bayes estimators in finite population samplings. Annals of Statistics, 35 (2). pp. 724-737. ISSN 0090-5364
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.
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