Quantile estimation of the selected exponential population

Abstract

Let π 1, π 2,…, π k be k independent exponential populations, where π i has the unknown location parameter ξ i , and the common unknown scale parameter σ. Let X i denote the minimum of a random sample of size n from π i , and X J =max{ X 1,…, X k }. Suppose the population corresponding to X J is selected. The problem of estimating a quantile θ J = ξ J + bσ, b⩾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 θ J , for all values of b⩾0, which is in contrast to the known results for the estimation of θ 1, based on the sample from π 1.