PA样本下连续型单参指数族参数的EB估计  

The empirical Bayes estimators of the parameter for the continuous one-parameter exponential family under PA samples

作　　者：王惠亚[1] 张涛[1] 郭鹏江[1] 

机构地区：[1]西北大学数学系,陕西西安710069

出　　处：《西北大学学报（自然科学版）》2008年第1期14-18,共5页Journal of Northwest University（Natural Science Edition）

基　　金：陕西省教育厅专项科研计划基金(03JK059)

摘　　要：目的研究PA样本情形下连续型单参指数族参数的经验Bayes估计。方法对密度函数及其导函数采用核估计的方法构造了参数的EB估计。结果在平方损失函数下,给出PA样本情形参数EB估计的收敛速度。结论在适当条件下,连续型单参指数族参数的经验Bayes估计,在PA样本下收敛速度可与iid样本及NA样本一样,任意接近O(n^(-1/2)。Aim To study the empirical Bayes estimators of the parameter for the continuous one-parameter exponential family. Methods A sequence of EB estimators for the parameter is constructed by the method of kernel estimation. Results Combing PA samples, the rates of convergence are obtained under quadratic loss function. Conclusion Under some suitable conditions, the convergence rates of EB estimators for the parameter in the case of PA samples can be terrified arbitrarily approaching to the best convergence rates O（n^-1/2） , as well as lid and PA samples.

关 键 词：PA样本 核估计 经验BAYES估计 收敛速度 

分 类 号：O211.4[理学—概率论与数理统计]