Inadmissibility of Usual and Mixed Estimators of Two Ordered Gamma Scale Parameters Under Reflected Gamma Loss Function

Abstract

Let Xi1, · · · , Xini be a random sample from a gamma distribution with known shape parameter νi > 0 and unknown scale parameter βi > 0, i = 1, 2, satisfying 0 < β1 β2 . We consider the class of mixed estimators for estimation of β1 and β2 under reflected gamma loss function. It has been shown that the minimum risk equivariant estimator of βi, i = 1,2, which is admissible when no information on the ordering of parameters are given, is inadmissible and dominated by a class of mixed estimators when it is known that the parameters are ordered. Also, the inadmissible estimators in the class of mixed estimators are derived. Finally the results are extended to some subclass of exponential family.