Asymptotic theory for bootstrapping the extremes

This paper considers asymptotic analysis of bootstrap distributions for the extremes from an iid sample. In contrast to the case of almost sure convergence to a fixed (normal) distribution in the case of the sample mean (finite variance case), the bootstrap distribution of an extreme tends in distribution to a random probability measure. These results are similar to the result for the bootstrap distribution of the sample mean in the infinite variance case where the underlying random variables are in the domain of attraction of a stable law with index αe(0,2).