正态-逆Wishart先验下多元线性模型中经验Bayes估计的优良性

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.

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

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 partlyunknown, the empirical Bayes estimators of the regressioncoefficient matrix and the error variance matrix are constructed. It is shown that the empirical Bayes estimators are superior to the corresponding least square estimatorsunder 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.