title: A local maximal inequality under uniform entropy.
abstract: We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant δ. The bound is expressed in the uniform entropy integral of the class at δ. The bound yields a rate of convergence of minimum contrast estimators when applied to the modulus of continuity of the contrast functions.
authors.affiliation: Department of Mathematics, Faculty of Sciences, Vrije Universiteit De Boelelaan 1081a, 1081 HV Amsterdam,  aad@cs.vu.nl.
authors.forename: Aad
authors.initials: A
authors.lastname: van der Vaart
authors.forename: Jon A
authors.initials: JA
authors.lastname: Wellner