Bootstrapping extremes of random variables under power normalization

This paper deals with the asymptotic of bootstrap for the distribution of extremes under power normalization when the underlying distribution belongs to the doll-lain of attraction of an extreme value distribution. We obtained the inconsistency, weak consistency and strong consistency of bootstrapping with appropriate choice of resample size when the normalizing constants are known. The same problem are investigated when the normalizing constants are unknown. The bootstrap for the joint distributions and the confidence intervals for the upper end of the distribution function F are obtained.