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We obtain a limit of a hierarchical Bayes estimator of a finite populationmean when the sample size is large. The limit is in the sense of ordinarycalculus, where the sample observations are treated as fixed quantities. Ourresult suggests a simple way to correct the hierarchical Bayes estimator toachieve design-consistency, a well-known property in the traditionalrandomization approach to finite population sampling. We also suggest threedifferent measures of uncertainty of our proposed estimator.

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