连续型单参数指数族参数的经验Bayes检验函数的收敛速度

doi:10.12341/jssms08446

系统科学与数学 ›› 2009, Vol. 29 ›› Issue (8): 1142-1152.DOI: 10.12341/jssms08446

• 论文 • 上一篇

连续型单参数指数族参数的经验Bayes检验函数的收敛速度

陈玲(1), 韦来生(2)

(1)中国科学技术大学统计与金融系, 合肥230026;安徽大学数学科学学院, 合肥230039;(2)中国科学技术大学统计与金融系, 合肥230026.

收稿日期:2006-10-10 修回日期:2009-05-12 出版日期:2009-08-25 发布日期:2009-08-25

PDF ( 483 ) 引用被引次数 ( 27 )

陈玲;韦来生. 连续型单参数指数族参数的经验Bayes检验函数的收敛速度[J]. 系统科学与数学, 2009, 29(8): 1142-1152.

CHEN Ling;WEI Laisheng. Convergence Rates of the Empirical Bayes Test Problem for Continuous One-Parameter Exponential Family[J]. Journal of Systems Science and Mathematical Sciences, 2009, 29(8): 1142-1152.

Convergence Rates of the Empirical Bayes Test Problem for Continuous One-Parameter Exponential Family

CHEN Ling(1), WEI Laisheng(2)

(1)Department of Statistics and Finance, USTC,Hefei 230026;School of Mathematical Science, Anhui University,Hefei 230039;(2)Department of Statistics and Finance, USTC, Hefei 230026.

Received:2006-10-10 Revised:2009-05-12 Online:2009-08-25 Published:2009-08-25

对独立同分布样本情形的连续型单参数指数族的单边假设检验问题,在线性损失下导出了单调的Bayes检验函数,构造了相应的经验Bayes(EB)检验函数. 在一定条件下, 获得的经验Bayes检验
函数的收敛速度可任意接近$O(n^{-1})$.最后给出了满足定理条件的两个例子.

关键词： 连续型单参数指数族, 独立同分布(iid)样本, 单调Bayes检验函数, EB检验函数, 收敛速度.

In this paper, the empirical Bayes (EB) one-sided test problem for the continuous one-parameter exponential family is considered. The monotone Bayes test rule is derived and the EB test rule is constructed by using the independent and identically distributed (iid) samples. The convergence rate for the proposed EB test rule is obtained. It is shown that the convergence rates of the proposed EB
test rules can arbitrarily close to $O(n^{-1})$ under suitable conditions. Finally, two examples concerning main result are given.

Key words: Continuous one-parameter exponential family, iid samples, monotone Bayes test rule, empirical Bayes test rules, convergence rates.

MR(2010)主题分类:

62C12
62F05

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