A paradoxical argument about domination

摘要

We consider the Bayes estimator of the mean vector theta of a multivariate normal distribution under uncertain prior information when the covariance matrix Sigma 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 theta 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. (C) 2019 Elsevier B.V. All rights reserved.