Reconciliation of Bayes and empirical Bayes interval estimation with application to SAE

Thomas M. Menino Convention & Exhibition Center 

Multilevel normal hierarchical models play an important role in developing statistical theory in multiparameter estimation for a wide range of applications. In this article, we propose a new reconciliation framework of the empirical Bayes and hierarchical Bayes approaches for interval estimation of random effects under a two-level normal model. Our framework shows that a second-order efficient empirical Bayes confidence interval, with empirical Bayes coverage error of order O(m^{-3/2}), can also be viewed as a credible interval whose posterior coverage is close to the nominal level, provided a carefully chosen prior-referred to as a 'matching prior'-is placed on the hyperparameters. While existing literature has examined matching priors that reconcile frequentist and Bayesian inference in various settings, this paper is the first to study matching priors with the goal of interval estimation of random effects in a two-level model. We obtain an area-dependent matching prior on the variance component that achieves a proper posterior under mild regularity conditions. The theoretical results in the paper are corroborated through a Monte Carlo simulation study and a real data analysis.

Credible interval

Empirical best linear unbiased prediction

Linear mixed model

Matching prior 

Survey Research Methods Section