多元线性模型中回归系数矩阵的可估函数和协方差阵的同时Bayes估计及优良性
发布时间：2018-12-21 17:38
【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.
[Abstract]:In this paper, the problem of Bayes estimation for multivariate linear models with non-column full rank design matrix is studied. Assuming that the regression coefficient matrix and covariance matrix have a normal inverse Wishart prior distribution, the estimable function of the regression coefficient matrix and the simultaneous Bayes estimation of the covariance matrix are derived by using the Bayes theory. Then under the Bayes Mean Square Error (BMSE) criterion and the Bayes Mean Square Error Matrix (BMSEM) criterion, it is proved that the Bayes estimation of estimable function and covariance matrix is superior to the generalized least square (Generalized Least Square,GLS) estimate. In addition, we study the superiority of Bayes estimators for estimable functions under Bayes Pitman Closeness (BPC) criterion. Finally, Monte Carlo simulation is carried out to verify the theoretical results.
【作者单位】： 安徽师范大学数学计算机科学学院;
【基金】：国家自然科学基金(11201005) 安徽师范大学研究生科研创新与实践项目(2014yks057)
【分类号】：O212.1
本文编号：2389237
[Abstract]:In this paper, the problem of Bayes estimation for multivariate linear models with non-column full rank design matrix is studied. Assuming that the regression coefficient matrix and covariance matrix have a normal inverse Wishart prior distribution, the estimable function of the regression coefficient matrix and the simultaneous Bayes estimation of the covariance matrix are derived by using the Bayes theory. Then under the Bayes Mean Square Error (BMSE) criterion and the Bayes Mean Square Error Matrix (BMSEM) criterion, it is proved that the Bayes estimation of estimable function and covariance matrix is superior to the generalized least square (Generalized Least Square,GLS) estimate. In addition, we study the superiority of Bayes estimators for estimable functions under Bayes Pitman Closeness (BPC) criterion. Finally, Monte Carlo simulation is carried out to verify the theoretical results.
【作者单位】： 安徽师范大学数学计算机科学学院;
【基金】：国家自然科学基金(11201005) 安徽师范大学研究生科研创新与实践项目(2014yks057)
【分类号】：O212.1
【相似文献】
相关期刊论文 前10条
1 刘小茂;矩阵损失下不可估函数的线性估计的可容许性[J];武汉汽车工业大学学报;2000年01期
2 喻胜华,何灿芝;一般Gauss-Markov模型中可估函数的线性Minimax估计[J];应用概率统计;2003年02期
3 喻胜华;二次损失下一般Gauss-Markov模型中可估函数的线性Minimax估计[J];应用数学学报;2003年04期
4 杨复兴;关于可估函数LS估计相和条件的一个问题[J];应用概率统计;2004年01期
5 李胜宏;周占功;;矩阵损失下多元Gauss-Markov模型中可估函数的线性Minimax估计[J];江苏科技大学学报(自然科学版);2010年01期
6 温忠麟;二次损失下可估函数的线性MINIMAX估计的性质及其应用[J];华南师范大学学报(自然科学版);1998年03期
7 徐礼文,喻胜华;一般正态线性模型中可估函数的线性Minimax估计[J];经济数学;2004年01期
8 武坤,刘军,唐义德,谢振中;GM估计的一个刻划及其应用[J];中南工业大学学报;1997年03期
9 温忠麟,杨镜华;正态线性模型中可估函数的Minimax估计[J];数学年刊A辑(中文版);1999年06期
10 姜峰;正态线性试验中可估函数的最小最大估计[J];菏泽师专学报;1999年04期
，本文编号：2389237
本文链接：https://www.wllwen.com/kejilunwen/yysx/2389237.html
