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

TL;DR

This paper analyzes the limit behavior of hierarchical Bayes estimators for finite population means as sample size grows, proposing a correction for design-consistency and methods to quantify uncertainty.

Contribution

It introduces a limit analysis of hierarchical Bayes estimators and proposes a simple correction to ensure design-consistency in finite population sampling.

Findings

Hierarchical Bayes estimators converge to a limit as sample size increases.

A correction method is proposed to achieve design-consistency.

Three measures of uncertainty for the corrected estimator are suggested.

Abstract

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.