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;韦来生

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

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中国科学院数学与系统科学研究院期刊网
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系统科学与数学 ›› 2009, Vol. 29 ›› Issue (8) : 1142-1152. DOI: 10.12341/jssms08446
论文

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)

作者信息 +

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

    CHEN Ling(1), WEI Laisheng(2)
Author information +
文章历史 +

摘要

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.

Abstract

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.

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.

Key words

Continuous one-parameter exponential family / iid samples / monotone Bayes test rule / empirical Bayes test rules / convergence rates.

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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. 系统科学与数学, 2009, 29(8): 1142-1152. https://doi.org/10.12341/jssms08446
CHEN Ling , WEI Laisheng. Convergence Rates of the Empirical Bayes Test Problem for Continuous One-Parameter Exponential Family. Journal of Systems Science and Mathematical Sciences, 2009, 29(8): 1142-1152 https://doi.org/10.12341/jssms08446
中图分类号： 62C12    62F05   
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