正态-逆Gamma先验下线性模型中回归系数和误差方差Bayes估计的改进  

Improvement of Bayes Estimation of Regression Coeffcients and Error Variance in Linear Model with Respect to Normal-Inverse Gamma Priors

作　　者：许凯[1] 何道江[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241003

出　　处：《吉林大学学报（理学版）》2014年第2期251-255,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11201005);全国统计科学研究计划重点项目(批准号:2013LZ17);安徽省自然科学基金(批准号:1308085QA13);安徽省高校自然科学研究重点项目(批准号:KJ2012A135)

摘　　要：在正态-逆Gamma先验下,研究线性模型中回归系数和误差方差Bayes估计的优良性,改进了已有的结果,去掉了附加条件.在Pitman准则下,证明回归系数的Bayes估计优于最小二乘估计(LSE),并讨论误差方差的Bayes估计在均方误差准则下相对于LSE的优良性.最后进行Monte Carlo模拟研究,进一步验证了理论结果.The superiority of Bayes estimation of regression coeffcients and error variance in linear model was studied based on normal-inverse Gamma priors.The existed results were complemented without the additive conditions.It was shown that the Bayes estimation of regression coefficients is superior to the least squares estimator （LSE ） under the Pitman closeness criterion. And the superiority of the Bayes estimation of error variance over LSE was also investigated in terms of the mean square error criterion. Finally, a Monte Carlo simulation was carried out to verify the theoretical results.

关 键 词：BAYES估计 最小二乘估计 BAYES PITMAN准则 均方误差准则 

分 类 号：O212.2[理学—概率论与数理统计]