Empirical Bayes Tests For Some Non-Exponential Distribution Family

摘要

Empirical Bayes tests for testing H(0): theta (less than or equal to) theta(0) against H1: theta (greater than) theta(0) in the distribution family having density f(x/theta) = Ia(x)/A(theta) for 0 (less than) x (less than) theta are considered under the linear loss. We construct the empirical Bayes tests delta(n) and Delta(n) and prove that both of them have a good asymptotic property. As a special case, taking a(x) = 1 leads to a result obtained by Karunamuni (1999). But our result gets rid of the condition that the critical point b(G) falls in some interval O, P0, where P0 (less than) theta(0) is a known constant.