New concentration inequalities for suprema of empirical processes

TL;DR

This paper introduces new concentration inequalities for the supremum of empirical processes based on low moment assumptions, broadening applicability beyond traditional boundedness or tail conditions.

Contribution

It provides the first concentration inequalities under weak moment conditions for empirical process suprema, even with large envelopes.

Findings

Concentration inequalities derived under low moment assumptions.

Applicable to cases with large envelopes.

Extends the scope of empirical process theory.

Abstract

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.