An inequality for uniform deviations of sample averages from their means

Abstract

Abstract We derive a new inequality for uniform deviations of averages from their means. The inequality is a common generalization of previous results of Vapnik and Chervonenkis [1974, Theory of Pattern Recognition. Nauka, Moscow] and Pollard [1995, Uniform ratio limit theorems for empirical processes, Scand. J. Statist. 22, 271–278]. Using the new inequality we obtain tight bounds for empirical loss minimization learning.