The admissible minimax estimator in Gauss–Markov model under a balanced loss function

Abstract

In this paper, we investigate the admissible minimax estimator (AME) of regression coefficient in Gauss–Markov model under a balanced loss function. In the class of homogeneous linear estimators, we obtain the AME under two occasions, respectively. We also prove that the AME is a shrinkage estimator of the best linear unbiased estimator (BLUE). Furthermore, we prove that the AME dominates the BLUE under certain conditions.

Keywords:

• admissible minimax estimator
• Gauss–Markov model
• balanced loss function

MSC:

• 62C15
• 62J12

Acknowledgements

We would like to thank the editors and the referees for their helpful suggestions to improve our paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was partially supported by the Natural Science Foundation of Jiangxi Province [20122BAB211007, 20144BAB2110001], Humanities and Social Science Planning Foundation in College of Jiangxi Province [TJ1401], and the National Social Science Foundation of China [12BTJ014].