Univ. Heidelberg
Statistics Group   Institute for Mathematics   Faculty of Mathematics and Computer Science   University Heidelberg
Ruprecht-Karls-Universität Heidelberg Institute for Mathematics Statistics of inverse problems Research Group
german english french



Publications
Cooperations
Research projects
Events
Teaching
Completed theses
People
Contact


Last edited on
Oct 17, 2023 by JJ
.
Thesis:
Bachelor in Mathematics 50%

Author:
Miriam Maurer

Title:
Adaptive Laguerre density estimation for mixed Poisson models

Supervisors:
Sergio Brenner Miguel and Jan JOHANNES

Abstract:
In non-life insurances a commonly used model is given by the Poisson process model. Due to dependencies on different quantities the assumption that the intensity is a fixed parameter is not reasonable in many applications. Therefore it makes sense to interpret the intensity as a random variable on the positive real line, which leads us to the more general mixed Poisson process model. In this thesis the unknown density f of the random intensity is estimated using an iid sample of the value of a mixed Poisson process at a fixed observation time. This is done by a penalized projection approach using the Laguerre basis. The focus is to introduce a data-driven selection rule for an adequate dimension parameter in order to deal with the upcoming bias-variance conflict. An upper bound of the L2-risk is obtained and a lower bound is provided, which proves the optimality of the estimator. Further the procedure is illustrated via a monte-carlo simulation.

References:
F. Comte and V. Genon-Catalot. Adaptive laguerre density estimation for mixed Poisson models. Electronic Journal of Statistics, 9(1):1113–1149, 2015.