Estimating quantiles of a selected exponential population

Suppose independent random samples are available from k exponential populations with a common location [theta] and scale parameters [sigma]1,[sigma]2,...,[sigma]k, 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.