| Auteur(s) |
Mélina Bec ( )1, Claire Lacour ()2 |
| Laboratoire |
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| Domaine |
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| Titre |
Adaptive kernel estimation of the Lévy density |
| Résumé |
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. |
| Langue du texte intégral |
Anglais |
| Date de production, écriture |
05/2012 |
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