中文摘要：

本文研究了在设计阵非列满秩情况下多元线性模型的Bayes估计问题.假定回归系数矩阵和协方差阵具有正态-逆Wishart先验分布,运用Bayes理论导出了回归系数矩阵的可估函数和协方差阵的同时Bayes估计.然后在Bayes Mean Square Error（BMSE）准则和Bayes Mean Square Error Matrix（BMSEM）准则下,证明了可估函数和协方差阵的Bayes估计优于广义最小二乘（Generalized Least Square,GLS）估计.另外,在Bayes Pitman Closeness（BPC）准则下研究了可估函数的Bayes估计的优良性.最后,进行了Monte Carlo模拟研究,进一步验证了理论结果.

英文摘要：

In this paper,the parameter estimation problem in a multivariate linear model is investigated when the design matrix is non-full rank,the joint prior of regression coefficient matrix and covariance matrix is assumed to be the normal-inverse Wishart distribution.By using the Bayes theory,the Bayes estimation of estimable function of regression coefficient matrix and covariance matrix are derived.Then we prove that the Bayes estimation of estimable function and covariance matrix are superior to the corresponding generalized least square（GLS） estimators under the criteria of Bayes mean squaxe error（BMSE） and Bayes mean square error matrix（BMSEM）.In addition,under the Bayes Pitman Closeness（BPC） criterion,the superiority of the Bayes estimation of estimable function is also investigated.Finally,a Monte Carlo simulation is carried out to verify the theoretical results.