Resampling methodologies and reliable tail estimation

Resampling methodologies, like the generalised jackknife and the bootstrap are importanttools for a reliable semi-parametric estimation of parameters of extreme or even rare events. Among these parameters we mention the extreme value index, the primary parameter in statistics of extremes, and the extremal index, a measure of clustering of extreme events. Most of the semi-parametric estimators of these parameters show the same type of behaviour: nice asymptotic properties, but a high variance for small k, the number of upper order statistics used in the estimation, a high bias for large k, and the need for an adequate choice of k. After a brief reference to some estimators of the aforementioned parameters and their asymptotic properties we present algorithms for an adaptive reliable estimation of the extreme value and extremal index