Empirical Bayes estimation for truncation parameters

This paper considers the empirical Bayes estimation under squared error loss for the truncation parameters with density functions f(1)(x(1)\ theta(1))= h(1) (x(1))/k(1)(theta(1)), a < theta(1) less than or equal to x(1) < b, or f(2)(x(2) \ theta(2)) = h(2)(x(2))/k(2)(theta(2)), a < x(2) less than or equal to theta(2) < b, where -infinity less than or equal to a less than or equal to b less than or equal to infinity. We propose the empirical Bayes estimator based on the relation between the Bayes estimator and the marginal distribution, respectively, for the two different distribution models. We then investigate the asymptotic optimality of the proposed empirical Bayes estimators and discuss two examples. (C) 2000 Elsevier Science B.V. All rights reserved.