PA样本下刻度指数族参数的EB检验  

The empirical Bayes test of the parameter for the scale-exponential family under PA samples

作　　者：郭鹏江[1] 王惠亚[1] 张涛[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《西北大学学报（自然科学版）》2009年第1期1-5,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资助项目(03JK059);国家自然科学基金部主任基金资助项目(08)

摘　　要：目的研究PA样本情形下刻度指数族参数的经验Bayes检验问题。方法对密度函数及其导函数采用核估计的方法构造EB检验函数。结果在加权线性损失下,给出PA样本情形参数EB检验函数渐近最优性及其收敛速度。结论在适当条件下,所构造的EB检验函数的收敛速度可与iid样本及NA样本一样,任意地接近O(n-12)。Aim To study the empirical Bayes test problem about the scale-exponential family by using weighted linear loss function. Methods A sequence of EB test functions for the parameter is constructed by the method of kernel estimation. Results Combing PA samples, asymptotic optimal properties of EB test functions are gotten and the rates of convergence are obtained under quadratic loss function. Conclusion Under some suitable conditions, the convergence rates can be terrified arbitrarily approaching to the best convergence rates O（n^-1/2）, as well as lid and NA samples.

关 键 词：PA样本 核估计 经验BAYES检验 收敛速度 

分 类 号：O211.4[理学—概率论与数理统计]