Shrinkage estimation in the two-way multivariate normal model

Abstract

A two-way multivariate normal model is proposed and attention is focused on estimation of the mean values when the common variance of the observations is unknown. A class of empirical Bayes estimators is proposed and mean-squared errors are given. A lower bound on the mean-squared error is found and related to risk asymptotics. A James-Stein-type estimator is derived and compared with its competitor--a modal estimator that is obtained from a hierarchical prior for the unknown parameters.