Some empirical Bayes estimators allowing for varying error variances

Abstract

SUMMARY For certain repetitive experiments where the parameters of interest vary randomly from experiment to experiment, improved estimators for the present values of the parameters can be obtained using the information from estimates in previous experiments. Martz & Krutchkoff (1969) provided empirical Bayes estimators for a multiple regression model with fixed error variance. Their resulte are extended to include the case in which the error variance is unknown and may vary from one experiment to the next. Similar empirical Bayes estimators are also provided for bivariate normal and analysis of variance models. Monte Carlo results are given to show that, in most cases, these estimators have smaller mean squared errors than the corresponding classical estimators.