On estimating the location parameter of the selected exponential population under the LINEX loss function

Abstract

Suppose that π1, π2,…,πk be k(≥ 2) independent exponential populations having unknown location parameters μ1, μ2, … , μk and known scale parameters σ1, … , σk. Let μ[k] = max{μ1, … , μk}. For selecting the population associated with μ[k], a class of selection rules (proposed by Arshad and Misra [Statistical Papers 57 (2016) 605–621]) is considered. We consider the problem of estimating the location parameter μS of the selected population under the criterion of the LINEX loss function. We consider three natural estimators δN,1, δN,2 and δN,3 of μS, based on the maximum likelihood estimators, uniformly minimum variance unbiased estimator (UMVUE) and minimum risk equivariant estimator (MREE) of μi ’s, respectively. The uniformly minimum risk unbiased estimator (UMRUE) and the generalized Bayes estimator of μS are derived. Under the LINEX loss function, a general result for improving a location-equivariant estimator of μS is derived. Using this result, estimator better than the natural estimator δN,1 is obtained. We also shown that the estimator δN,1 is dominated by the natural estimator δN,3. Finally, we perform a simulation study to evaluate and compare risk functions among various competing estimators of μS.