On asymptotic optimality of bayes empirical bayes estimators

In an empirical Bayes decision problem, a prior distribution ≱ is placed on a one-dimensfonal family G of priors Gw, wεΩ, to produce a Bayes empirical Bayes estimator, The asymptotic optimaiity of the Bayes estimator is established when the support of ≱ is Ω and the marginal distributions Hw have monotone likelihood ratio and continuous Kullback-Leibler information number.