On Bayes Linear Unbiased Estimator Under the Balanced Loss Function

Abstract

In this paper, the Bayes linear unbiased estimator (Bayes LUE) is derived under the balanced loss function. Moreover, the superiority of Bayes LUE over ordinary least square estimator is studied under the mean square error matrix criterion and Pitman closeness criterion. Furthermore, we compare Bayes LUE under the balanced loss function with Bayes LUE under the quadratic loss function.

Keywords:

• balanced loss function
• Bayes linear unbiased estimator
• linear model
• mean square error matrix criterion
• Pitman closeness criterion

Mathematics Subject Classification:

• Primary 62-02
• Secondary 62C10, 62F15, 62F35, 62J05

Acknowledgments

The authors wish to thank an editor, an associate editor, and two referees for their valuable comments and constructive suggestions which greatly improved the presentation of the paper.

Funding

Qiu’s research was partially supported by NSFC-11171058 and NBRPC-2011CB403203. Luo’s research was partially supported by NSFC-11271317, NSF of Zhejiang Y6110615 and LY12A01017. Zheng’s research was partially supported by NECT-11-0616, NSFC-11071035 and the Fundamental Research Funds for the Central Universities.