一类离散型单参数指数族参数的双侧的经验Bayes检验问题

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

一类一维离散型单参数指数族参数的单侧的经验Bayes(EB)检验问题已有研究,但关于这类分布族的双边的EB检验问题尚无结果,本文研究这一问题,本文构造了参数的EB检验的判决函数,并且获得了它的渐近最优性和收敛速度。在文末给出定理说明了在一些情形下,加上适当的条件,精确的收敛速度可以达到n^(-1)。

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.