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Last edited on
Oct 18, 2021 by JJ
.
Thesis:
Bachelor in Mathematics

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.