Empirical Bayes estimation of the truncation parameter with Linex loss

This paper deals with the empirical Bayes estimation of the truncation position of the truncated family under the Liner loss. Nonparametric empirical Bayes estimator is proposed and its asymptotic optimality and rate are investigated. Under certain mild conditions without any differentiability assumption on either the prior or the marginal distribution, it is shown that the proposed empirical Bayes estimator is asymptotically optimal with convergence rate given. Simulation results on the performance of the proposed empirical Bayes estimator are also presented.