| 连续型单参数指数族参数的经验Bayes检验函数的收敛速度 |
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| 引用本文： | 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. |
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| 作者姓名： | 陈玲 韦来生 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金，中国科学院知识创新工程重要方向项目 |
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| 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.
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| 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. |
| 收稿时间： | 2006-10-10 |
| 修稿时间： | 2009-5-12 |
CONVERGENCE RATES OF THE EMPIRICAL BAYES TEST PROBLEM FOR CONTINUOUS ONE-PARAMETER EXPONENTIAL FAMILY |
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| 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. |
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| Authors: | CHEN Ling WEI Laisheng |
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| Institution: | (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. |
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| 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 EBtest rules can arbitrarily close to $O(n^{-1})$ under suitable conditions. Finally, two examples concerning main result are given. |
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| Keywords: | Continuous one-parameter exponential family iid samples monotone Bayes test rule empirical Bayes test rules convergence rates |
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