- Thesis:
- Master in Mathematics
- Author:
- Sophie Eyben
- Title:
- Concentration inequalities for Poisson point processes
- Supervisors:
- Jan JOHANNES
- Abstract:
- In this thesis we study concentration inequalities for maxima of Poisson point processes. In the first part of the thesis, we prove such concentration inequalities, whereby we prove the inequalities for right-hand and left-hand side deviations from its mean separately. The proofs are based on classic results for concentration inequalities, on certain properties of the Poisson point processes, such as the infinite divisibility and on Ledoux’s entropy method. We use these inequalities in the second part for adaptive intensity estimation. The aim is to estimate an intensity function of n observed i.i.d realizations of a Poisson point process and study the maximum risk of the estimator.
- Reference:
- Kroll, M. Concentration inequalities for Poisson point processes with application to adaptive intensity estimation, arXiv:1612.07901, 2016.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |