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

doi:10.3969/j.issn.1000-5641.2017.01.001

华东师范大学学报(自然科学版)

• 数学 • 下一篇

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

贺磊，徐静

安徽师范大学数学计算机科学学院, 安徽芜湖 241003

收稿日期:2015-12-29 出版日期:2017-01-25 发布日期:2017-01-13
通讯作者: 贺磊, 男, 硕士研究生, 研究方向为 Bayes 统计推断. E-mail: wallhelei@163.com.
基金资助:
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)

The superiority of Bayes estimators of the estimable function of regression coefficient matrix and the covariance matrix in multivariate linear model

HE Lei, XU Jing

College of Mathematics and Computer Science, Anhui Normal University, Wuhu Anhui 241003, China

Received:2015-12-29 Online:2017-01-25 Published:2017-01-13

摘要/Abstract

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.

关键词: 可估函数, 正态--逆 Wishart 先验, BMSE 准则, BMSEM 准则; BPC 准则

Abstract:

In this paper, the parameter estimation problem in a multivariate linear model is investigated when the design matrix is non-full rank, the joint prior of regression coefficient matrix and covariance matrix is assumed to be the normal-inverse Wishart distribution. By using the Bayes theory, the Bayes estimation of estimable function of regression coefficient matrix and covariance matrix are derived. Then we prove that the Bayes estimation of estimable function and covariance matrix are superior to the corresponding generalized least square (GLS) estimators under the criteria of Bayes mean square error (BMSE) and Bayes mean square error matrix (BMSEM). In addition, under the Bayes Pitman Closeness (BPC) criterion, the superiority of the Bayes estimation of estimable function is also investigated. Finally, a Monte Carlo simulation is carried out to verify the theoretical results.

Key words: estimable function, normal-inverse Wishart prior, BMSE criterion, BMSEM criterion, BPC criterion

贺磊，徐静. 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[J]. 华东师范大学学报(自然科学版), doi: 10.3969/j.issn.1000-5641.2017.01.001.

HE Lei, XU Jing. The superiority of Bayes estimators of the estimable function of regression coefficient matrix and the covariance matrix in multivariate linear model[J]. Journal of East China Normal University(Natural Sc, doi: 10.3969/j.issn.1000-5641.2017.01.001.

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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

The superiority of Bayes estimators of the estimable function of regression coefficient matrix and the covariance matrix in multivariate linear model

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