正态-逆Wishart先验下多元线性模型中经验Bayes估计的优良性  

Superiority of Empirical Bayes Estimators in Multivariate Linear Model with Respect to Normal-Inverse Wishart Priors

作　　者：许凯[1] 何道江[1] 徐兴忠[2] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241000 [2]北京理工大学数学与统计学院,北京100081

出　　处：《数学年刊（A辑）》2014年第3期267-284,共18页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11201005;No.11071015);全国统计科学研究计划重点项目(No.2013LZ17);安徽省自然科学基金(No.1308085QA13)的资助

摘　　要：在正态-逆Wishart先验下研究了多元线性模型中参数的经验Bayes估计及其优良性问题.当先验分布中含有未知参数时,构造了回归系数矩阵和误差方差矩阵的经验Bayes估计,并在Bayes均方误差(简称BMSE)准则和Bayes均方误差阵(简称BMSEM)准则下,证明了经验Bayes估计优于最小二乘估计.最后,进行了Monte Carlo模拟研究,进一步验证了理论结果.In this paper,the authors investigate the empirical Bayes estimation of parameters and its superiority in multivariate linear model with respect to normal-inverse Wishart priors.When the parameters of prior distribution are partly unknown,the empirical Bayes estimators of the regression coefficient matrix and the error variance matrix are constructed.It is shown that the empirical Bayes estimators are superior to the corresponding least square estimators under the criteria of Bayes mean square error（BMSE for short）and Bayes mean square error matrix（BMSEM for short）.Finally,a Monte Carlo simulation is carried out to verify the theoretical results.

关 键 词：正态逆Wishart先验 矩阵t分布 参数经验Bayes估计 最小二乘估计 BMSE准则 BMSEM准则 

分 类 号：O212.8[理学—概率论与数理统计]