The use of empirical Bayes estimators in a linear regression model

Abstract

New estimators for the parameters in the linear regression model are presented, using not only the usual random sample of observations, but also past experience in the form of previous estimates of parameters in similar but independent situations. The regression parameters are considered to be random variables. Bayes estimators are given for a squared error loss function. Even though the prior density of the parameter is unknown, the Bayes estimator can be written in terms of the marginal density of a sufficient statistic. This marginal density can be estimated empirically, thus forming the empirical Bayes estimator. Results of Monte Carlo simulation of empirical Bayes estimators are given which show that, even with a few past experiences, the empirical Bayes estimators have smaller mean squared errors than do the ordinary least-squares estimators, which use only current information.