| 刻度指数族参数的经验Bayes检验函数收敛速度的改进 |
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| 引用本文： | 周雁,韦来生.刻度指数族参数的经验Bayes检验函数收敛速度的改进[J].高校应用数学学报(A辑),2008,23(2):219-226. |
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| 作者姓名： | 周雁 韦来生 |
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| 作者单位： | 中国科学技术大学,统计与金融系,安徽合肥,230026 |
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| 基金项目： | 中国科学院知识创新工程项目 |
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| 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.
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| 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 |
| 文章编号： | 1000-4424(2008)02-0219-08 |
| 修稿时间： | 2006年10月24 |
Improvement of convergence rates for the empirical Bayes test problem in scale exponential family |
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| ZHOU Yan,Wei Lai-sheng.Improvement of convergence rates for the empirical Bayes test problem in scale exponential family[J].Applied Mathematics A Journal of Chinese Universities,2008,23(2):219-226. |
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| Authors: | ZHOU Yan Wei Lai-sheng |
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| Abstract: | 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 (PA) samples and lid samples.Finally,an example concerning main results is given. |
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| Keywords: | scale exponential family NA sample monotone Bayes test rule empirical Bayes test convergence rate |
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