华东师范大学学报(自然科学版) ›› 2013, Vol. 2013 ›› Issue (1): 24-29, 53.

• 应用数学与基础数学 • 上一篇    下一篇

矩阵损失下贝叶斯线性无偏估计及其稳健性

邱红兵1,  罗 季2   

  1. 1. 广东工业大学~~应用数学学院, 广州 510520;
    2. 浙江财经学院~~数学与统计学院, 杭州 310018
  • 收稿日期:2011-10-01 修回日期:2012-02-01 出版日期:2013-01-25 发布日期:2013-01-18

Bayesian linear unbiased estimator and its robustness under the matrix loss function

QIU Hong-bing 1,  LUO Ji 2   

  1. 1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China;
    2. School of Mathematics and Statistics School, Zhejiang University of Finance and Economics, Hangzhou 310018, China
  • Received:2011-10-01 Revised:2012-02-01 Online:2013-01-25 Published:2013-01-18

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摘要： 证明了, 在一般线性模型中,
未知参数在二次损失下的贝叶斯线性无偏估计也是矩阵损失下的贝叶斯线性无偏估计.
讨论了贝叶斯线性无偏估计关于误差分布的稳健性,
给出了未知参数的贝叶斯线性无偏估计是最优估计的充分必要条件.

关键词: 线性模型, 贝叶斯线性无偏估计, 稳健性

Abstract: It was proved that the Bayesian linear unbiased estimator
of the unknown parameters in a general linear model under the
quadratic loss function is also the Bayesian linear unbiased
estimator under the matrix loss function. The robustness of the
Bayesian linear unbiased estimator of the unknown parameter in terms
of error distributions was also discussed; moreover, the necessary
and sufficient conditions are obtained, under which the Bayesian
linear unbiased estimator of the unknown parameters hold its
optimality.

Key words: linear model, Bayesian linear unbiased estimator, robustness

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