Admissibility under the LINEX loss function in non-regular case

Abstract

In the statistical estimation theory, sufficient conditions for admissibility of estimators have been discussed mostly under quadratic loss function. Recently, under the LINEX loss function, sufficient conditions were developed in some families of distributions. However, they do not include some typical non-regular distributions so that the dimension of the minimal sufficient statistic is two. The purpose of this paper is to give sufficient conditions for admissibility of estimators in such non-regular distributions under the LINEX loss function. Some examples are also given.