Weak convergence and Glivenko-Cantelli results for empirical processes of u-statistic structure

AbstractEmpirical processes of U-statistic structure indexed by Vapnik-Chervonenkis classes of sets are studied for independent, but not necessarily identically distributed observations. Glivenko-Cantelli and weak convergence results are obtained by using a representation of these processes as an average of certain empirical processes. This generalizes a theorem of Helmers, Janssen and Serfling (1985) and includes the corresponding results for the empirical process