Empirical and Hierarchical Bayes Competitors of Preliminary Test Estimators in Two Sample Problems

Abstract

We consider the problem of estimation of μ1 when it is suspected that μ1 ≈ μ2 based on independent samples from Np (μ1,σ2V1) and Np(μ2,σ2V2). We assume V1, V2 known but σ2 unknown. First, the EB estimator is derived and its Bayesian and frequentist properties are studied. Second, a modified EB estimator is proposed and shown to dominate a preliminary test estimator. Finally, a hierarchical Bayes approach is proposed as an alternative to EB estimators.