Admissibility of Estimators of Two Ordered Gamma Scale Parameters under Entropy Loss Function

Suppose that a random sample of size ni is drawn from a gamma distribution with known shape parameter νi > 0 and unknown scale parameter βi > 0, i = 1, 2, satisfying 0 < β1 ≤ β2. In estimation of β1 and β2 under the entropy loss function, we consider the class of mixed estimators of β1 and β2. It is shown that a subclass of mixed estimators of βi beats the usual estimators Xi/νi , i = 1, 2, and the inadmissible estimators in the class of mixed estimators are derived. Also the asymptotic efficiency of mixed estimators relative to the usual estimators are obtained. Finally the results are extended to a subclass of the scale parameter exponential family and the family of transformed chi-square distributions.