On the design-consistency property of hierarchical Bayes estimators in finite population sampling

Details On the design-consistency property of hierarchical Bayes estimators in finite population sampling On the design-consistency property of hierarchical Bayes estimators in finite population sampling

2007-08-14

arxiv.org/abs/0708.1890v1

Annals of Statistics 2007, Vol. 35, No. 2, 724-737

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000001262 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000001262

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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