Concentration bounds for sampling without replacement and Hoeffding statistics

TL;DR

This paper establishes sharper Bennett-type concentration bounds for empirical processes and Hoeffding statistics when sampling without replacement, improving the theoretical understanding of their concentration behavior.

Contribution

It introduces improved concentration bounds for empirical processes and Hoeffding statistics under sampling without replacement, enhancing previous theoretical results.

Findings

Sharper Bennett-type concentration bounds derived

Enhanced understanding of empirical process behavior

Improved theoretical guarantees for Hoeffding statistics

Abstract

We prove a Bennett-type concentration bound for suprema of empirical processes based on sampling without replacement and a corresponding bound in the case of an arbitrary Hoeffding statistics. We improve on the previous results of such type, providing a sharper concentration profile.