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

Let xi1...xi n i be a random sample from a gammadistribution with known shape parameter vi > 0 and unknown scaleparameter (β > 0, i = 1,2, satisfying 0 < β1 « β2. we consider the classof mixed estimators for estimation of (31 and (32 under reflected gammaloss function. it has been shown that the minimum risk equivariantestimator of βi, i = 1,2, which is admissible when no information on the ordering of parameters are given, is inadmissible and dominatedby a class of mixed estimators when it is known that the parametersare ordered. also, the inadmissible estimators in the class of mixedestimators are derived. finally the results are extended to some subclassof exponential family.