| 线性模型中回归系数和误差方差的同时Bayes估计的优良性 |
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| 引用本文： | 陈玲,韦来生. 线性模型中回归系数和误差方差的同时Bayes估计的优良性[J]. 数学年刊A辑(中文版), 2011, 32(6): 763-774 |
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| 作者姓名： | 陈玲 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;安徽大学数学科学学院; |
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| 基金项目： | 国家自然科学基金(No11071232); 安徽大学青年科研基金(No2011KJQN1002)资助的项目 |
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| 摘 要： | 在线性模型中回归系数与误差方差具有正态-逆Gamma先验时,导出了回归系数与误差方差的同时Bayes估计.在均方误差矩阵准则和Bayes Pitman closeness准则下,研究了回归系数的Bayes估计相对于最小二乘(LS)估计的优良性,还讨论了误差方差的Bayes估计在均方误差准则下相对于LS估计的优良性.
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| 关 键 词： | 线性模型 Bayes估计 最小二乘估计 均方误差(矩阵)准则 Bayes Pitman closeness准则 |
Superiorities of Simultaneous Bayes Estimation of Regression Coefficients and Error-Variance in Linear Model |
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| CHEN Ling and WEI Laisheng. Superiorities of Simultaneous Bayes Estimation of Regression Coefficients and Error-Variance in Linear Model[J]. Chinese Annals of Mathematics, 2011, 32(6): 763-774 |
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| Authors: | CHEN Ling and WEI Laisheng |
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| Affiliation: | CHEN Ling~1 WEI Laisheng~2 1 Department of Statistics and Finance,University of Science and Technology of China,Hefei 230026,China,School of Mathematical Science,Anhui University. Hefei 230039,China. 2 Corresponding author.Department of Statistics and Finance,China. |
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| Abstract: | The simultaneous Bayes estimators of regression coefficients and error-variance are derived in linear model under the normal-invert Gamma prior distributions.The superiorities of the Bayes estimator over the least squares(LS) estimator for regression coefficients are investigated in terms of the mean square error matrix criterion and Bayes Pitman closeness criterion,and the superiority of the Bayes estimator of error-variance over LS estimator is also discussed under the mean square error criterion. |
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| Keywords: | Linear model Bayes estimation Least squares estimation Mean square error(matrix) criterion Bayes Pitman closeness criterion |
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