• 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

1. (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

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. (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

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.

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