Estimation After Selection From Gamma Populations With Unequal Known Shape Parameters

Abstract

Let be independent gamma populations, where the population has an unknown scale parameter and known shape parameter . We call the population associated with the best population. For the goal of selecting the best population, Misra and Arshad (2014) proposed a class of selection rules for the case of (possibly) unequal shape parameters. In this article, we consider the problem of estimating the mean of the population selected by a fixed selection rule , under a scale-invariant loss function. We derive the uniformly minimum variance unbiased estimator (UMVUE). Two other natural estimators and , which are respectively the analogs of the UMVUE and the best scale invariant estimators of for the component problem, are studied. We show that is generalized Bayes with respect to a noninformative prior distribution, and is also minimax when k = 2. The UMVUE and the natural estimator are shown to be inadmissible, and better estimators are obtained. A numerical study on the performance of various estimators indicates...