线性模型中回归系数和误差方差的同时Bayes估计的优良性

Superiorities of Simultaneous Bayes Estimation of Regression Coefficients and Error-Variance in Linear Model

在线性模型中回归系数与误差方差具有正态-逆Gamma先验时,导出了回归系数与误差方差的同时Bayes估计.在均方误差矩阵准则和Bayes Pitman closeness准则下,研究了回归系数的Bayes估计相对于最小二乘(LS)估计的优良性,还讨论了误差方差的Bayes估计在均方误差准则下相对于LS估计的优良性.

The simultaneous Bayes estimators of regression coefficients and error-variance are derived in linear model under the normal-invert Gamma prior distributions.The superiorities of the Bayes estimator over the least squares（LS） estimator for regression coefficients are investigated in terms of the mean square error matrix criterion and Bayes Pitman closeness criterion,and the superiority of the Bayes estimator of error-variance over LS estimator is also discussed under the mean square error criterion.