A Note on the Estimation of Restricted Scale Parameters of Gamma Distributions

Abstract

First, we find an admissible estimator of a scale parameter of Gamma distribution which is bounded from above. We also consider the simultaneous estimation of p scale parameters of Gamma distributions which are bounded from above. Next, we consider the simultaneous estimation of two ordered scale parameters of two Gamma distributions in terms of mean square error (MSE). 　　　Finally, we consider the estimation of linear functions of two ordered scale parameters of Gamma distributions. Chang and Shinozaki (2002) have considered this problem and have given a necessary and sufficient condition on the ratio of two coefficients which guarantees that maximum likelihood estimator (MLE) and modified MLE dominate the crude unbiased estimator (UE) and individually admissible estimator, respectively, in terms of MSE. Here we compare another type of order restricted estimators suggested by Vijayasree etc. (1995) with individually admissible estimator. We give a sufficient condition on coefficients which guarantees that the restricted estimators suggested by Vijayasree etc. (1995) improve the individually admissible estimator under MSE.