Nonparametric adaptive estimation for pure jump Lévy processes
F. Comte, V. Genon-Catalot (2010)
Annales de l'I.H.P. Probabilités et statistiques
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This paper is concerned with nonparametric estimation of the Lévy density of a pure jump Lévy process. The sample path is observed at discrete instants with fixed sampling interval. We construct a collection of estimators obtained by deconvolution methods and deduced from appropriate estimators of the characteristic function and its first derivative. We obtain a bound for the -risk, under general assumptions on the model. Then we propose a penalty function that allows to build an adaptive...