Hierarchical Bayes estimators of the error variance in one-way ANOVA models

Abstract

For estimating the error variance in the one-way ANOVA problem, the paper proposes a class of hierarchical Bayes (HB) estimators which overcomes the Neyman-Scott problem. A subclass of these HB estimators is found to be minimax. The resulting class of priors is strictly contained within the class of HB priors which meets Peers's criterion of matching asymptotically the posterior probability of a credible set and the frequentist probability up to a certain order.