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

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.

Keywords:

• Poisson point process
• concentration inequality
• entropy method
• adaptive estimation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Financial support by the Deutsche Forschungsgemeinschaft (DFG) through the Research Training Group RTG 1953 is gratefully acknowledged. The final preparation of the manuscript has also been supported by the research grant DFG DE 502/27-1 of the German Research Foundation (DFG).