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

Abstract

Suppose that a random sample of size n_i is drawn from a gamma distribution with known shape parameter ν_i> 0 and unknown scale parameter β_i> 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 β_i beats the usual estimators X_i/ν_i , 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.