Stein控制估计量的损失函数之估计

ESTIMATED LOSS FOR STEIN’S DOMINATING ESTIMATOR

本文获得了［１］中正态分布Ｎ，（θ，Ｉ）均值θ的估计量的风险之无偏估计满足［２］中提出的条件（Ⅰ）的充分条件与必要条件，特别Ａ当为幂等阵时得到了充要条件，这是［２］提出的一个问题。本文还给出了的损失的另一种估计，它满足［２］中的条件（Ⅰ）和（Ⅱ）。

In this paper , we consider the open problem put by Berger and Lu(1987),i.e. ,whether the un-biased estimator of risk of the dominating estimator proposed by Stein(1981)satisfies condition(Ⅰ) in[2]or not. We obtain some sufficient conditions that it satisfies(Ⅰ) or does’tsatisfy( Ⅰ ).Especially,when A is an idenpotent matrix ,we obtain a necessary and sufficientondi-tion. We also propose another stimated loos for the estimator.