Inadmissibility of Usual and Mixed Estimators of Two Ordered Gamma Scale Parameters Under Re°ected Gamma Loss Function

Let Xi1; ¢ ¢ ¢ ;Xini be a random sample from a gamma distribution with known shape parameter ?i > 0 and unknown scale parameter ¯i > 0, i = 1; 2, satisfying 0 < ¯1 6 ¯2. We consider the class of mixed estimators for estimation of ¯1 and ¯2 under re°ected gamma loss function. It has been shown that the minimum risk equivariant estimator of ¯i, 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.