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AbstractSuppose independent random samples are available from k exponential populations with a common location θ and scale parameters σ1,σ2,…,σk, respectively. The population corresponding to the largest sample mean is selected. The problem is to estimate a quantil...

AbstractSuppose independent random samples are available from k exponential populations with a common location θ and scale parameters σ1,σ2,…,σk, respectively. The population corresponding to the largest sample mean is selected. The problem is to estimate a quantile of the selected population. In this paper, we derive the uniformly minimum variance unbiased estimator (UMVUE) using (U-V) method of Robbins (in: Gupta and Berger (Eds.), Statistical Decision Theory and Related Topics — IV, Vol. 1, Springer, New York, 1987, pp. 265–270) and Rao–Blackwellization. Further, a general inadmissibility result for affine equivariant estimators is proved. As a consequence, an estimator improving upon the UMVUE with respect to the squared error and the scale invariant loss functions is obtained.

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