Admissibility and Minaxity Results in the Estimation Problem of Exponential Quantiles

Abstract

The estimation problem of the quantiles $\xi + b\sigma$ of an exponential distribution with unknown location-scale parameter $(\xi, \sigma)$ is considered. We establish the admissibility of the traditional (best equivariant) estimator for quadratic loss when $n^{-1} \leq b \leq 1 + n^{-1}$ where $n$ is the sample size. For $b > 1 + n^{-1}$ a class of minimax procedures is found. This class contains generalized Bayes rules and one of them is shown to be admissible within the class of scale-equivariant procedures.