Admissible and Minimax Estimators of a Lower Bounded Scale Parameter of a Gamma Distribution under the Entropy Loss Function

This paper is concerned with admissible and minimax estimation of scale parameter µ of a gamma distribution under the entropy loss function, when it is known that µ > a for some known a > 0. An admissible minimax estimator of µ, which is the pointwise limit of a sequence of Bayes estimators, is derived. Also, the admissible estimators and the only minimax estimator of µ in the class of truncated linear estimators are obtained. Finally, the results are extended to a subclass of scale parameter exponential family and the family of transformed chi-square distributions.