Uniform concentration bounds for frequencies of rare events

TL;DR

This paper introduces new concentration inequalities for empirical distributions, focusing on rare events within low probability regions, with explicit constants for practical numerical comparisons.

Contribution

It derives novel Vapnik-Chervonenkis type bounds for rare event frequencies, providing explicit constants for better numerical applicability.

Findings

Derived new concentration inequalities for rare events.

Provided explicit constants for practical use.

Focused on maximal deviations over Borel set classes.

Abstract

New Vapnik and Chervonenkis type concentration inequalities are derived for the empirical distribution of an independent random sample. Focus is on the maximal deviation over classes of Borel sets within a low probability region. The constants are explicit, enabling numerical comparisons.