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| HAL : hal-00583221, version 3 |
| arXiv : 1205.4692 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (05-04-2011) | v2 (21-05-2012) | v3 (13-02-2013) |
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| Adaptive pointwise estimation for pure jump Lévy processes |
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| Mélina Bec 1Claire Lacour 2 |
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| (02/2013) |
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| This paper is concerned with adaptive kernel estimation of the Lévy density N(x) for bounded-variation pure-jump Lévy processes. The sample path is observed at n discrete instants in the "high frequency" context (\Delta = \Delta(n) tends to zero while n\Delta tends to infinity). We construct a collection of kernel estimators of the function g(x)=xN(x) and propose a method of local adaptive selection of the bandwidth. We provide an oracle inequality and a rate of convergence for the quadratic pointwise risk. This rate is proved to be the optimal minimax rate. We give examples and simulation results for processes fitting in our framework. We also consider the case of irregular sampling. |
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| 1 : | Mathématiques appliquées Paris 5 (MAP5) |
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CNRS : UMR8145 – Université Paris V - Paris Descartes |
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| 2 : | Laboratoire de Mathématiques d'Orsay (LM-Orsay) |
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CNRS : UMR8628 – Université Paris XI - Paris Sud |
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| Domaine | : | Mathématiques/Statistiques Statistiques/Théorie |
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| Adaptive Estimation – High frequency – Pure jump Lévy process – Nonparametric Kernel Estimator |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00583221, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00583221 | |
| oai:hal.archives-ouvertes.fr:hal-00583221 | |
| Contributeur : Mélina Bec | |
| Soumis le : Mardi 12 Février 2013, 21:45:00 | |
| Dernière modification le : Mercredi 13 Février 2013, 14:37:21 | |
