New concentration inequalities for suprema of empirical processes

Johannes C. Lederer, Sara A. van de Geer

Published 2011-11-15, updated 2014-10-22Version 2

While effective concentration inequalities for suprema of empirical processes exist under boundedness or strict tail assumptions, no comparable results have been available under considerably weaker assumptions. In this paper, we derive concentration inequalities assuming only low moments for an envelope of the empirical process. These concentration inequalities are beneficial even when the envelope is much larger than the single functions under consideration.