Sufficient conditions for the admissibility under the LINEX loss function in non-regular case

Abstract

Consider an estimation problem under the LINEX loss function in one-parameter non-regular distributions where the endpoint of the support depends on an unknown parameter. The purpose of this paper is to give sufficient conditions for a generalized Bayes estimator of a parametric function to be admissible. Also, it is shown that the main result in this paper is an extension of the quadratic loss case. Some examples are given.

Keywords:

• admissibility
• generalized Bayes estimator
• LINEX loss function
• non-regular distribution

AMS Subject Classification :

• 62C15
• 62F10
• 62F15

Acknowledgements

The author would like to express thanks to the referees for careful reading which are useful in improving the paper. This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B), 21700309, 2009.