Rate of convergence in the central limit theorem for empirical processes

Abstract

Let ℕ n and\(\mathbb{B}_\mu \) be an empirical process and a generalized Brownian bridge, respectively, indexed by a class ℱ of real measurable functions. From the central limit theorem for empirical processes it follows that for allr≥0. In this paper, assuming the class ℱ to be countably determined, under certain conditions we obtain an estimate for some constantC. Vapnik-Cervonenkis class and the indicators of lower left orthants provide examples of classes ℱ considered here.