Prior information in regression: to choose or not to choose?

Abstract

Stein-rule estimators for the parameters of the linear regression model are simple, nonlinear transformations of the usual least squares/maximum likelihood estimator. Under certain design related conditions Stein-rule estimators are known to be minimax and dominate the MLE under quadratic loss functions. In order to obtain quadratic risk improvements over the MLE using a Stein-rule the user must choose some target value for 3 or more of the parameters. If the chosen target is not reasonably close to the actual value of the parameters, risk gains over the MLE will be small. When several alternative pieces of nonsample information (targets) exist, using the best target results in the greatest overall risk gain. George (1986) has developed a multiple shrinkage estimator which uses all of the possible targets. Each target receives a different weight in the shrinkage estimator. The weights are a function of the target's probable proximity to the true parameter vaue. In this case, no choice need be made. Anothe...