ON THE ESTIMATION OF HIGH QUANTILES

We consider the quantile estimator x(p) from Dekkers, Einmahl and de Haan Annals of Statistics 17, 1989, for n-->infinity, p = p(n) --> 0 and np(n) --> 0 (n-->infinity). This is the situation of interest when one wants to protect against a calamity which has not yet occurred. Asymptotic normality is proved under appropriate conditions. The results are applied to high water levels outside Delfzijl on the Dutch coast, and are supplemented by a small simulation study.