刻度指数族参数的经验Bayes检验函数收敛速度的改进  

Improvement of convergence rates for the empirical Bayes test problem in scale exponential family

作　　者：周雁[1] 韦来生[1] 

机构地区：[1]中国科学技术大学统计与金融系,安徽合肥230026

出　　处：《高校应用数学学报（A辑）》2008年第2期219-226,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：中科院知识创新工程重要方向项目(KJCX3-SYW-S02)

摘　　要：在加权线性损失下导出了刻度指数族中参数单调的Bayes检验函数,利用同分布负相协(NA)样本情形概率密度函数及其导数的核估计构造了经验Bayes(EB)检验函数,获得了EB检验函数的收敛速度.在适当的条件下,这一收敛速度可任意接近O(n^(-1)),改进了文献中已有的结果.对同分布正相协(PA)样本和独立同分布(iid)样本情形,亦可获得类似结论.最后给出了一个满足文中主要结果的例子.The monotone Bayes test rules for scale exponential family are derived under weighted linear loss function,the EB test rules are constructed by using kernel estimation method in the case of negatively associated (NA) samples,and the convergence rates are obtained.The convergence rates for the proposed EB test rules can be arbitrarily close to O(n^(-1)) under suitable conditions,which has improved the given result in the literature.Similar results can be obtained for the cases of the positively associated (P...

关 键 词：刻度指数族 NA样本 单调的Bayes检验 经验BAYES检验 收敛速度 

分 类 号：O212.8[理学—概率论与数理统计]