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Limit theorems for extreme value estimates of point processes boundaries

Stéphane Girard 1 Ludovic Menneteau 2
1 IS2 - Statistical Inference for Industry and Health
Inria Grenoble - Rhône-Alpes, LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558
Abstract : We give sufficient conditions to establish central limit theorems and moderate deviation principles for support estimates of Poisson point processes- . The considered estimates write as linear combinations of extreme values of the point process. Our results are illustrated on four particular cases: Haar and trigonometric series estimates, Faber-Shauder estimate and kernel estimate. A hierarchy between these estimators is proposed by comparing their optimal convergence rates.
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https://hal.inria.fr/inria-00072222
Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 8:08:30 PM
Last modification on : Monday, February 10, 2020 - 4:36:45 PM
Long-term archiving on: : Sunday, April 4, 2010 - 9:05:24 PM

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  • HAL Id : inria-00072222, version 1

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Stéphane Girard, Ludovic Menneteau. Limit theorems for extreme value estimates of point processes boundaries. [Research Report] RR-4366, INRIA. 2002. ⟨inria-00072222⟩

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