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

doi:10.3969/j.issn.1000-5641.2017.01.001

Journal of East China Normal University(Natural Sc

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

Abstract

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

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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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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