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| Fiche détaillée | Preprint, Working Paper, Document sans référence, etc. |
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| Versions disponibles : | v1 (05-04-2011) | v2 (21-05-2012) | v3 (13-02-2013) |
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| Adaptive kernel estimation of the Lévy density |
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| Mélina Bec1Claire Lacour2 |
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| This paper is concerned with adaptive kernel estimation of the Lévy density $N(x)$ for 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_n $ 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. |
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| 1 : | MAP5 - Mathématiques appliquées Paris 5 |
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| 2 : | LM-Orsay - Laboratoire de Mathématiques d'Orsay |
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| hal-00583221, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00583221 | |
| oai:hal.archives-ouvertes.fr:hal-00583221 | |
| Contributeur : Mélina Bec | |
| Soumis le : Lundi 21 Mai 2012, 12:17:51 | |
| Dernière modification le : Lundi 21 Mai 2012, 21:09:05 | |
