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Preprints, Working Papers, ... Year : 2021

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.
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Dates and versions

hal-03402380 , version 1 (25-10-2021)

Identifiers

  • HAL Id : hal-03402380 , version 1

Cite

B Bobbia, C Dombry, Davit Varron. A Donsker and Glivenko-Cantelli theorem for random measures linked to extreme value theory. 2021. ⟨hal-03402380⟩
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