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

doi:10.3969/j.issn.1000-5641.2017.01.001

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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 Sciences), 2017, (1): 1-10. doi: 10.3969/j.issn.1000-5641.2017.01.001

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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 Sciences), 2017, (1): 1-10. 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

doi: 10.3969/j.issn.1000-5641.2017.01.001

HE Lei,
XU Jing

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

Received Date: 2015-12-29
Publish Date: 2017-01-25

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.
- estimable function,
- normal-inverse Wishart prior,
- BMSE criterion,
- BMSEM criterion,
- BPC criterion

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References(16)

References

[1]	RAO C R. Linear Statistical Inference and Its Applications[M]. New York: Wiley, 1973.
[2]	陈敏, 韦来生. 线性模型中回归系数的可估函数和误差方差的同时Bayes估计的优良性[J]. 应用数学学报, 2014, 37(5): 865-877. http://www.cnki.com.cn/Article/CJFDTOTAL-YYSU201405009.htm
[3]	王松桂, 史建红, 尹素菊, 等. 线性模型引论[M]. 北京: 科学出版社, 2004.
[4]	BOX G E P, TIAO G C. Bayesian Inference in Statistical Analysis[M]. Massachusetts: Addison-Wesley, 1973.
[5]	XU K, HE D J. The superiority of Bayes estimators in a multivariate linear model with respect to normal-inverse Wishart prior[J].Acta Mathematicae Applicatae Sinica, English Series, 2015, 31(6): 1003-1014. doi: 10.1007/s10114-015-3649-2
[6]	ZHANG W P, WEI L S, CHEN Y. The superioritities of Bayes linear unbiased estimator in multivariate linear models[J]. Acta Mathematicae Applicatae Sinica, English Series, 2012, 28(2): 383-394. doi: 10.1007/s10255-012-0150-x
[7]	ANDERSON T W. An Introduction to Multivariate Statistical Analysis[M]. New Jersey: John Wiley and Sons, 2003.
[8]	许凯, 何道江, 徐兴忠. 正态--逆Wishart先验下多元线性模型中经验Bayes估计的优良性[J]. 数学年刊, 2014, 35A(3): 267-284. http://www.cnki.com.cn/Article/CJFDTOTAL-SXNZ201403002.htm
[9]	ZHANG X D. Matrix Analysis and Application[M]. Beijing: Tsinghua University Press, 2004.
[10]	LIU J S. An Introduction to Wishart Distributions[M]. Beijing: Science Press, 2005.
[11]	PITMAN E J G. The closest estimates of statistical parameters[J]. Proc Camb Phil Soc, 1937, 33: 212-222. doi: 10.1017/S0305004100019563
[12]	RAO C R. Some comments on the minimum mean square as criterion of estimation statistics and related topics[M]//Statistics and Related Topics. Amsterdam: North-Holland Publishing Co, 1981: 123-143.
[13]	RAO C R, KEATING J P, MASON R L. The Pitman nearness criterion and determination[J]. Communications in Statistics--Theory and Methods, 1986, 15: 3173-3191. doi: 10.1080/03610928608829302
[14]	KEATING J P, MASON R L, SEN P K. Pitman's measure of closeness: A comparison of statistical estimators[M]//Society for Industrial and Applied Mathematics. Philadelphia: [s.n.], 1993: 571-581.
[15]	WEI L S, ZHANG W P. The superiorities of Bayes linear minimun risk estimation in linear mode[J]. Communications in Statistics-Theory and Methods, 2007, 36: 917-926. doi: 10.1080/03610920601036333
[16]	陈玲, 韦来生. 线性模型中回归系数和误差方差的同时,Bayes,估计的优良性[J]. 数学年刊, 2011, 32A(6): 763-774. http://www.cnki.com.cn/Article/CJFDTOTAL-SXNZ201106016.htm