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 Adaptive kernel estimation of the Lévy density
 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.
 hal-00583221, version 2 http://hal.archives-ouvertes.fr/hal-00583221 oai:hal.archives-ouvertes.fr:hal-00583221 From: Mélina Bec <> Submitted on: Monday, 21 May 2012 12:17:51 Updated on: Monday, 21 May 2012 21:09:05