Admissibility and minimaxity results in the estimation problem of exponential quantiles (Q1080577)

Let \(X_ 1,X_ 2,...,X_ n\) be a random sample from an exponential distribution with unknown location-scale parameter (\(\xi\),\(\alpha)\) and consider the estimation of the quantiles \(\xi +b\alpha\). The author proves that the traditional estimator (best equivariant) is admissible under quadratic loss when \(n^{-1}\leq b\leq 1+n^{-1}\). Moreover, a class of minimax procedures is found when \(b>1+n^{-1}\). This class is shown to contain generalized Bayes rules and one of them is proved to be admissible within the class of scale-equivariant procedures.