Empirical Bayes Estimators in a Multiple Linear Regression Model

Abstract

Empirical Bayes estimators for the parameters in the general linear regression model are presented. These estimators by-pass exact knowledge of the prior distribution of the parameters by means of supplementary information from similar independent experiments. Indexing quantities are obtainned which summarize the information containe in a typical experimental situation, an Monte Carlo simulation is employed to determine the degree of mean square improvement of empirical Bayes estimators over maximum likelihood. Particular emphasis is given to the simple non-orthogonal linear regression model.