| 正态总体均值和误差方差同时的经验Bayes估计 |
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| 作者姓名： | 仇丽莎 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, 合肥 230026 |
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| 基金项目： | 国家自然科学基金 (11071232, 11271346, 11271347)资助 |
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| 摘 要： | 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.
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| 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 |
| 收稿时间： | 2012-07-08 |
| 修稿时间： | 2012-10-22 |
Simultaneous empirical Bayes estimation for mean and error variance in normal distribution |
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| Authors: | QIU Li-Sha WEI Lai-Sheng |
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| Institution: | University of Science and Technology of China, Hefei 230026, China |
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| Abstract: | 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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| Keywords: | normal distribution mean parameters error variance parametric empirical Bayes estimation (PEBE) mean-square error (MSE) criterion |
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