A Donsker and Glivenko‐Cantelli theorem for random measures linked to extreme value theory
研究了一类与外部随机现象条件相关的随机点测度，证明了在均匀熵条件下Glivenko-Cantelli和Donsker定理成立，并给出了极值理论和最近邻规则中的应用。
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.