Concentration inequalities for Poisson point processes with application to adaptive intensity estimation

TL;DR

This paper develops concentration inequalities for Poisson point processes and demonstrates their application in adaptive intensity estimation, providing new tools for statistical analysis of such processes.

Contribution

It introduces novel concentration inequalities for maxima of empirical processes related to Poisson point processes, enhancing statistical inference methods.

Findings

Derived new concentration inequalities for Poisson processes.

Applied inequalities to improve adaptive intensity estimation.

Validated the inequalities through practical application.

Abstract

We derive concentration inequalities for maxima of empirical processes associated with Poisson point processes. The proofs are based on a careful application of Ledoux's entropy method. We demonstrate the utility of the obtained concentration inequalities by application to adaptive intensity estimation.