A paradoxical argument about domination

Abstract

We consider the Bayes estimator of the mean vector θ of a multivariate normal distribution under uncertain prior information when the covariance matrix Σ is unknown. We use the plug-in estimator S to obtain the approximate Bayes as well as the empirical Bayes estimators under a multiparameter linear exponential loss function. Then the risks of the proposed estimators are compared and dominating the unbiased estimator of θ with respect to Bayes risk is discussed. The empirical Bayes estimator is compared with the best of the estimators in Srivastava and Ehsanes Saleh (2005) by means of a simulation study. The empirical Bayes estimator is shown to have smaller mean absolute LINEX errors for a wide range of parameter values. The biases do not appear to differ much.