Bootstrapping the Stein-Rule Estimators

In this paper we consider the Stein-rule estimator and the positive-part Stein-rule estimator for the mean of a multivariate normal distribution and analyze the validity of the bootstrap methods for these estimators. We show that the conventional bootstrap is not always consistent and propose an alternative bootstrap method which is consistent when the conventional bootstrap is inconsistent. We also show the consistency of the m out of n bootstrap. Moreover, we propose an consistent bootstrap method based on a pre-test. Our simulation results show the validity of the proposed bootstrap in various setups.