PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Model selection for Poisson processes
Lucien Birgé
In: Asymptotics: particles, processes and inverse problems, Festschrift for Piet Groenenboom IMS Lecture Notes - Monographs series , 55 . (2007) Institute of Mathematical Statistics , Beachwood, USA , pp. 32-64. ISBN 0-940600-71-4


Our purpose in this paper is to apply the general methodology for model selection based on T-estimators developed in Birg\'e (2006a) to the particular situation of the estimation of the unknown mean measure of a Poisson process. We introduce a Hellinger type distance between finite positive measures to serve as our loss function and we build suitable tests between balls (with respect to this distance) in the set of mean measures. As a consequence of the existence of such tests, given a suitable family of approximating models, we can build T-estimators for the mean measure based on this family of models and analyze their performances. We provide a number of applications to adaptive intensity estimation when the square root of the intensity belongs to various smoothness classes. We also give a method for aggregation of preliminary estimators.

EPrint Type:Book Section
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
ID Code:2882
Deposited By:Lucien Birgé
Deposited On:25 February 2008