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VOL. 55 | 2007 Model selection for Poisson processes
Lucien Birgé

Editor(s) Eric A. Cator, Geurt Jongbloed, Cor Kraaikamp, Hendrik P. Lopuhaä, Jon A. Wellner


Our purpose in this paper is to apply the general methodology for model selection based on T-estimators developed in Birgé 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.


Published: 1 January 2007
First available in Project Euclid: 4 December 2007

zbMATH: 1176.62082
MathSciNet: MR2459930

Digital Object Identifier: 10.1214/074921707000000265

Primary: 62G05, 62M30
Secondary: 41A45, 41A46, 62G10

Rights: Copyright © 2007, Institute of Mathematical Statistics


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