Admissibility in general Gauss–Markov model with respect to an ellipsoidal constraint under weighted balanced loss

Abstract

Under weighted balanced loss function, we obtain the best linear unbiased estimator of regression coefficient in general Gauss–Markov model and discuss the admissibility of linear estimators of the regression coefficient with respect to an ellipsoidal constraint. We establish necessary and sufficient conditions for the admissibility of the linear estimators $Ay$($Ay+a$) among the class of homogeneous and inhomogeneous linear estimators, respectively.

Keywords:

• Gauss–Markov model
• weighted balanced loss
• best linear unbiased estimator
• ellipsoidal constraint
• admissibility

MSC:

• 62C05
• 62F10

Acknowledgements

The authors thank the editor and referees for their constructive comments and helpful suggestions on a previous version of the manuscript, which have greatly improved the article.

Authors’ contributions

All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

Additional information

Funding

This work was partially supported by National Natural Science Foundation of China (61374082).