渐近最优的经验贝叶斯决策(英文)  

Asymptotically Optimal Empirical Bayes Decision

作　　者：陈家清[1] 陈志强[1] 张智敏[1] 刘次华[2] 

机构地区：[1]武汉理工大学统计学系,湖北武汉430070 [2]华中科技大学数学与统计学院,湖北武汉430074

出　　处：《应用数学》2013年第1期95-103,共9页Mathematica Applicata

基　　金：Supported by the Foundamental Research Funds for the Central Universities of China(2010-1a-027);the Posterdoctoral Funds of China(20100471168)

摘　　要：本文在加权线性损失下讨论一类广义指数分布刻度参数的经验贝叶斯检验问题.利用核密度估计函数构造单调的经验贝叶斯检验函数,在适当的条件下证明所构造的检验函数的渐近最优性并获得其收敛速度.该收敛速度可以任意接近O(n-1).最后,给出一个例子用以验证本文的主要结果是合理的.In this paper, the empirical Bayes decision problem of scale parameter for a generalized exponential distribution under weighed linear loss function has been discussed. The monotone empir- ical Bayes test （EBT） rules are constructed by using the kernel-type density method. The asymptoti- cally optimal property and convergence rates for the proposed EBT rules are obtained under suitable conditions. Their convergence rate can arbitrary close to O（n-1 ） and an example is given to verify the main results of this paper which are reasonable.

关 键 词：广义指数分布 经验贝叶斯检验 渐近最优性 收敛速度 

分 类 号：O212.1[理学—概率论与数理统计]