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.Selection rule Quantiles Uniformly minimum variance unbiased estimator Affine equivariant estimator Inadmissible estimator