The Central Limit Theorem for Empirical Processes on Vapnik-Cervonenkis Classes

Abstract

Sufficient conditions, which under weak additional assumptions are also necessary, are found for the central limit theorem for empirical processes indexed by classes of functions which have the Vapnik-Cervonenkis property. This improves an earlier theorem of Pollard (1982a), and leads to necessary and sufficient conditions for the CLT for weighted empirical processes indexed by Vapnik-Cervonenkis classes of sets.