线性模型中回归系数和误差方差同时的经验Bayes估计及其优良性  

The Superiorities of Simultaneous Empirical Bayes Estimation for the Regression Coefficients and Error-Variance in Linear Model

作　　者：陈玲[1,2] 韦来生[1] 

机构地区：[1]中国科学技术大学统计与金融系,合肥230026 [2]安徽大学数学科学学院,合肥230039

出　　处：《应用概率统计》2012年第6期583-600,共18页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金(11071232,11171001);安徽大学青年科研基金(2010KJQN1002);安徽大学博士科研启动经费(023033190168)资助

摘　　要：在线性模型中,当先验分布中超参数部分未知时,构造了回归系数和误差方差的同时参数型经验Bayes估计(PEBE).在均方误差矩阵(MSEM)准则下,讨论了回归系数的PEBE相对于最小二乘估计(LSE)的优良性;在均方误差(MSE)准则下讨论了误差方差的PEBE相对于其LSE的优良性.当先验分布中超参数全部未知时,重新构造了回归系数和误差方差的同时PEBE,并给出了它们在MSE准则下相对LSE优良性的模拟结果.When the hyperparameters of prior distribution are partly known in linear model, the simultaneous parametric empirical Bayes estimators （PEBE） of the regression coefficients and error variance are constructed. The superiority of PEBE over the least squares estimator （LSE） of regression coefficients is investigated in terms of the the mean square error matrix （MSEM） criterion, and the superiority of PEBE over LSE of the error variance is discussed under the the mean square error （MSE） criterion. Finally, when all hyperparameters are unknown, the PEBE of regression coefficients and error variance are reconstructed and the superiority of them over LSE under the MSE criterion are studied by simulation methods.

关 键 词：线性模型 参数型经验Bayes估计 最小二乘估计 均方误差(矩阵)准则 模拟结果 

分 类 号：O212.1[理学—概率论与数理统计]