Optimal critical regions for pre-test estimators using a Bayes risk criterion (Q2266311)

Optimal critical regions for pre-test estimators are developed in the context of the normal linear regression model with a conjugate prior, where the criterion is Bayes risk and where the pre-testing involves a single coefficient. When prior information is neutral regarding the sign of the coefficient, it is shown that the optimal include-exclude decision involves no pre-testing. When prior information is weighted toward a particular sign, pre-testing is appropriate but the optimal critical regions are quite different from those associated with the traditional pre-test estimator.