中文摘要：

在线性模型中回归系数与误差方差具有正态-逆Gamma先验分布,且假定设计阵非列满秩的情形下,导出了回归系数的可估函数与误差方差同时的Bayes估计.分别在均方误差矩阵（MSEM）准则和Bayes Pitman Closeness（BPC）准则下,研究了回归系数可估函数的Bayes估计相对于最小二乘（LS）估计的优良性,讨论了误差方差的Bayes估计在均方误差（MSE）准则下相对于LS估计的优良性.

英文摘要：

Under the normal-invert Gamma prior distributions, the simultaneous Bayes estimators of the estimable function of regression coefficients and error-variance are derived in linear model with the non-full rank design matrix. The superiorities of the Bayes estimator over the least squares （LS） estimator for the estimable function of regression coefficients are investigated respectively in terms of the mean square error matrix （MSEM） criterion and Bayes Pitman Closeness （BPC） criterion, and the superiority of the Bayes estimator of error variance over its LS estimator is ;also discussed under the mean square error （MSE） criterion.