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)...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.展开更多
In this paper, the multivariate linear model Y = XB＋e, e ～ Nm×k（0, ImΣ） is considered from the Bayes perspective. Under the normal-inverse Wishart prior for （BΣ）, the Bayes estimators are derived. The sup...In this paper, the multivariate linear model Y = XB＋e, e ～ Nm×k（0, ImΣ） is considered from the Bayes perspective. Under the normal-inverse Wishart prior for （BΣ）, the Bayes estimators are derived. The superiority of the Bayes estimators of B and Σ over the least squares estimators under the criteria of Bayes mean squared error （BMSE） and Bayes mean squared error matrix （BMSEM） is shown. In addition, the Pitman Closeness （PC） criterion is also included to investigate the superiority of the Bayes estimator of B.展开更多
文摘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.
基金Supported by National Natural Science Foundation of China(Grant Nos.11201005,11071015)the Foundation of National Bureau of Statistics(Grant No.2013LZ17)the Natural Science Foundation of Anhui Province(Grant No.1308085QA13)
文摘In this paper, the multivariate linear model Y = XB＋e, e ～ Nm×k（0, ImΣ） is considered from the Bayes perspective. Under the normal-inverse Wishart prior for （BΣ）, the Bayes estimators are derived. The superiority of the Bayes estimators of B and Σ over the least squares estimators under the criteria of Bayes mean squared error （BMSE） and Bayes mean squared error matrix （BMSEM） is shown. In addition, the Pitman Closeness （PC） criterion is also included to investigate the superiority of the Bayes estimator of B.
