收稿日期: 2012-07-08
修回日期: 2012-10-22
网络出版日期: 2013-07-15
基金资助
国家自然科学基金 (11071232, 11271346, 11271347)资助
Simultaneous empirical Bayes estimation for mean and error variance in normal distribution
Received date: 2012-07-08
Revised date: 2012-10-22
Online published: 2013-07-15
在正态分布情形下,假定均值参数和误差方差服从正态-逆伽马分布先验时,导出了均值参数和误差方差的 Bayes 估计, 利用历史样本构造了它们的参数型经验 Bayes 估计 (PEBE). 在均方误差(MSE)准则下,分别获得均值参数和误差方差相对于一致最小方差无偏估计 (UMVUE) 的优良性.最后,给出一个有关主要结果的注释.
关键词： 正态分布; 均值参数; 误差方差; 参数型经验Bayes估计; 均方误差准则
仇丽莎 , 韦来生 . 正态总体均值和误差方差同时的经验Bayes估计[J]. 中国科学院大学学报, 2013 , 30(4) : 454 -461 . DOI: 10.7523/j.issn.2095-6134.2013.04.005
In the normal distribution, by assuming that the parameters of mean and error variance have the normal inverse-Gamma distribution, the simultaneous Bayes estimators of mean and error variance are derived. By using historical samples, the parametric empirical Bayes estimators (PEBE) are constructed. Superiorities of PEBE over UMVUE in mean parameter and error variance are obtained in terms of the MSE criterion. Finally, we give a remark on the main results.
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