The Empirical Bayes Estimation of the Location Parameter in Double-Exponential Family under the LINEX Loss Function

In this paper, we derive the Bayes estimator of the location parameter in double-exponential family under the LINEX loss function, and then construct the corresponding empirical Bayes estimator. It is shown that the empirical Bayes estimator is asymptotically optimal with convergence rate being , , where 1/2<r<1-1/(2s), while is a given integer. Finally, an example is demonstrated.