Abstract

We extend extreme value statistics to independent data with possibly very different distributions, whereby the extreme value index of the average distribution can be negative, zero, or positive. We present novel asymptotic theory for the moment estimator and find that the asymptotic variance can be much smaller than that in the i.i.d. case. We also unravel the improved performance of high quantile and endpoint estimators. In case of a heavy tail, we ameliorate the Hill estimator. We present applications to lifespans of monozygotic twins and to earthquake energies.