EMPIRICAL BAYES TWO-SIDED TEST PROBLEMS ABOUT ONE-PARAMETER DISCRETE EXPONENTIAL FAMILIES

Empirical Bayes （EB） one-sided test problem about discrete one-parameter exponential familiy has been discussed. But the EB two-sided test problems of this family has not been considered. In this paper we study this problem. We construct the EB test decision rule. Furthermore we get its asymptotically optimal property and the convergence rates. Finally we obtain a theorem to explain why the exact rates of convergence can achieve O(n^-1) for one ease under suitable conditions.