Quantile estimation of the selected exponential population

Abstract

Let pi(1), pi(2),..., pi(k) be k independent exponential populations, where pi(i) has the unknown location parameter xi(i), and the common unknown scale parameter sigma. Let X-i denote the minimum of a random sample of size n from pi(i), and X-J = max{X-1,..., X-k}. Suppose the population corresponding to X-J is selected. The problem of estimating a quantile theta(J) = xi(J) + bsigma, b greater than or equal to 0, of the selected population is considered. The properties of the natural estimators are investigated. We derive a sufficient condition, based on the method of differential inequalities, for an estimator in the class of scale-equivariant estimators to be inadmissible. As a special case, we obtain improved estimators over the natural estimator of theta(J), for all values of b greater than or equal to 0, which is in contrast to the known results for the estimation of theta(1), based on the sample from pi(1). (C) 2002 .