Stein-type shrinkage quantile estimation

The simultaneous asymptotic estimation theory of quantiles is considered for an arbitrary population. The Stein-type estimator and its positive version are considered. The relative merits of the proposed estimators are compared with those of the usual estimator using asymptotic quadratic distributional risk under local alternatives. It is shown that both proposed estimators are asymptotically superior to the classical estimator. Further, it is demonstrated that the Stein-type estimator is dominated by its positive part.