Estimation after selection from exponential populations with unequal scale parameters

Consider $$k$$ k ( $$\ge $$ ≥ 2) exponential populations having unknown guarantee times and known (possibly unequal) failure rates. For selecting the unknown population having the largest guarantee time, with samples of (possibly) unequal sizes from the $$k$$ k populations, we consider a class of selection rules based on natural estimators of the guarantee times. We deal with the problem of estimating the guarantee time of the population selected, using a fixed selection rule from this class, under the squared error loss function. The uniformly minimum variance unbiased estimator (UMVUE) is derived. We also consider two other natural estimators $$\varphi _{N,1}$$ φ N , 1 and $$\varphi _{N,2}$$ φ N , 2 which are, respectively, based on the maximum likelihood estimators and UMVUEs for component problems. The estimator $$\varphi _{N,2}$$ φ N , 2 is shown to be generalized Bayes. We further show that the UMVUE and the natural estimator $$\varphi _{N,1}$$ φ N , 1 are inadmissible and are dominated by the natural estimator $$\varphi _{N,2}$$ φ N , 2 . A simulation study on the performance of various estimators is also reported.