A Donsker and Glivenko-Cantelli theorem for random measures linked to extreme value theory
Abstract
We consider a class of random point measures that share properties with empirical measures when conditioned to another exogenous random phenomenon. We investigate the validity of some Glivenko-Cantelli and Donsker theorems for such random measures. In this setup, we prove that the usual conditions on uniform entropy numbers are strong enough to derive these two theorems. A bootstrap Donsker theorem is also proved. Some applications of these results are also presented in the framework of extreme value theory and nearest-neighbor rules.
Domains
Statistics [math.ST]
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