On the Admissibility of Linear Estimators in a Multivariate Normal Distribution Under LINEX Loss Function

Abstract

Consider an estimation problem of a linear combination of population means in a multivariate normal distribution under LINEX loss function. Necessary and sufficient conditions for linear estimators to be admissible are given. Further, it is shown that the result is an extension of the quadratic loss case as well as the univariate normal case.

Keywords:

• Admissibility
• LINEX loss function
• Multivariate normal distribution

Mathematics Subject Classification:

• Primary 62C15
• Secondary 62F10, 62F15

Acknowledgments

The authors would like to express our thanks to the referee for the careful reading which was useful in improving the article. This research was partially supported by Grant-in-Aid for Scientific Research (C) (No. 18540136), Japan Society for the Promotion of Science.