Estimation of the scale parameter of a selected gamma population with unequal shape parameters under stein loss function

Negin Mahlooji and Nader Nematollahi

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 18, 6573-6596

Abstract: The problem of estimation of the parameter of a selected population arises when we encounter with several populations and would like to estimate the parameter of the best (worst) selected population. Suppose Xi1,Xi2,…,Xini,i=1,…,k be k(≥2) independent random samples drawn from populations Π1,Π2,…,Πk, respectively, where observations from Πi have a Gamma(αi,θi)-distribution with unequal known shape parameters αi,i=1,…,k. In this paper, we use a selection rule to select the best (worst) population, and estimate the best (worst) scale parameter θS (θJ) of the selected population under the Stein loss function. The uniformly minimum risk unbiased (UMRU) estimators of θS and θJ are obtained. A sufficient condition for inadmissibility of scale-invariant estimators of θS (θJ) is obtained and it is shown that the UMRU estimator of θS (θJ) is inadmissible. For k = 2, a sufficient condition for minimaxity of a given estimator of θS (θJ) is obtained, and the generalized Bayes estimator of θS is shown to be minimax. Finally, the risk functions of the various competing estimators are compared numerically, and a real data is provided to compute the proposed estimates and their expected risks.

Date: 2023
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DOI: 10.1080/03610926.2022.2032167

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