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数学进展 - 2016, Vol. 45(2): 280-288
研究论文
Lomax 分布族形状参数的经验Bayes检验函数的收敛速度
Convergence Rates for Empirical Bayes Tests for the Shape Parameter of Lomax Distribution Family

黄金超1,凌能祥2
HUANG Jinchao1, LING Nengxiang2

1.滁州职业技术学院基础部,~滁州, 安徽, 239000;
2. 合肥工业大学数学学院,~合肥, 安徽, 230009
1. Basic Course Department, Chuzhou Vocational Technology College, Chuzhou, Anhui, 239000, P. R. China;
2. School of Mathematics, Hefei University of Technology, Hefei, Anhui, 230009,P. R. China

收稿日期: 2014-09-30
出版日期: 2016-03-10
2016, Vol. 45(2): 280-288
DOI: 10.11845/sxjz.2014158b


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摘要 

本文研究了Lomax 分布族形状参数的经验 Bayes (EB) 检验问题, 利用密度函数的递归核估计, 构造了形状参数的单调的经验 Bayes 检验函数, 在适当的条件下, 得到了收敛速度, 且收敛速度的阶可无限趋近于 $O(n^{-1})$. 最后给出一个满足定理条件的例子.

Abstract

In this paper, the empirical Bayes (EB) test problem of shape parameter for Lomax distribution family is investigated. By using the recursive kernel estimation of density function, the monotone empirical Bayes test rules are constructed. And convergence rates are obtained under suitable conditions. The convergence rates can be arbitrarily close to $O(n^{-1})$. Finally, an example concerning with the main result is given.

PACS:  O212.1  
基金资助:

安徽省高校自然科学基金资助项目 (No. KJ2013Z252, No. KJ2015A345).

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