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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (5): 523-533.doi: 10.3969/j.issn.1005-3085.2018.05.004

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一类连续型单参数指数族参数的经验Bayes检验函数的收敛速度

黄金超   

  1. 滁州职业技术学院基础部，安徽  滁州  239000
  • 收稿日期:2016-09-12 接受日期:2017-11-03 出版日期:2018-10-15 发布日期:2018-12-15
  • 基金资助:
    安徽省高校自然科学基金重点项目(KJ2015A345)；安徽省高校优秀青年骨干人才国内访学研修项目(gxfx2017225)；滁州职业技术学院院级规划重点项目(YJZ-2016-01).

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

HUANG Jin-chao   

  1. Basic Course Department, Chouzhou Vocational And Technical College, Chuzhou, Anhui 239000
  • Received:2016-09-12 Accepted:2017-11-03 Online:2018-10-15 Published:2018-12-15
  • Supported by:
    The Key Projects of Natural Science Foundation of Universities and Colleges in Anhui Province (KJ2015A345); the Research Project of Outstanding Young Talents for Domestic Visiting in Anhui Universities and Colleges (gxfx2017225); the Key Project of Chuzhou Vocational and Technical College (YJZ-2016-01).

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摘要： 本文研究了一类连续型单参数指数族参数的经验Bayes检验问题．利用独立同分布样本下概率密度函数的递归核估计和Bayes检验函数的单调性，重新构造一类连续型单参数指数族参数的EB检验函数．通过修改EB检验函数的构造方法，构造了单调的Bayes检验函数．在一定的条件下，获得了EB检验函数的收敛速度，改进了现有文献中的收敛速度阶的结果．最后给出满足定理条件的数值算例．

关键词: 密度函数的核估计, 单调的Bayes检验, 经验Bayes检验, 收敛速度

Abstract: The empirical Bayes test problem of parameter for a class of continuous one-parameter exponential family is considered in this paper. By using the recursive kernel esti-mation of probability density function and monotonicity of Bayes test function in the case of independent and identically distributed samples, the EB test function in established for a class of continuous one-parameter exponential family. By the construction method of modifying EB test function, the monotone Bayes test function are constructed. In addition, convergence rates of EB test function are obtained under the suitable conditions, and the results of convergence rate order are improved. Finally, a numerical example is presented to verify the conditions of the theorem.

Key words: the kernel estimation of density function, monotone Bayes test, the empirical Bayes test, convergence rates

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