Concentration around the mean for maxima of empirical processes

Abstract

In this paper we give optimal constants in Talagrand's concentration inequalities for maxima of empirical processes associated to independent and eventually nonidentically distributed random variables. Our approach is based on the entropy method introduced by Ledoux.Comment: Published at http://dx.doi.org/10.1214/009117905000000044 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org