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February 2012 Nonparametric inference for discretely sampled Lévy processes
Shota Gugushvili
Ann. Inst. H. Poincaré Probab. Statist. 48(1): 282-307 (February 2012). DOI: 10.1214/11-AIHP433

Abstract

Given a sample from a discretely observed Lévy process X = (Xt)t≥0 of the finite jump activity, the problem of nonparametric estimation of the Lévy density ρ corresponding to the process X is studied. An estimator of ρ is proposed that is based on a suitable inversion of the Lévy–Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of ρ over suitable classes of Lévy triplets. The corresponding lower bounds are also discussed.

Soit un échantillon d’un processus de Lévy X = (Xt)t≥0 à activité finie observé en temps discret, le problème d’estimation non-paramétrique de la densité de Lévy ρ est étudié. Un estimateur de ρ est proposé basé sur une inversion de Fourier de la formule de Lévy–Khintchine et un principe de plug-in. Les principaux résultats de cet article portent sur la majoration du risque de l’estimateur de ρ pour des classes de triplets de Lévy. La minoration du risque est aussi discutée.

Citation

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Shota Gugushvili. "Nonparametric inference for discretely sampled Lévy processes." Ann. Inst. H. Poincaré Probab. Statist. 48 (1) 282 - 307, February 2012. https://doi.org/10.1214/11-AIHP433

Information

Published: February 2012
First available in Project Euclid: 23 January 2012

zbMATH: 1235.62121
MathSciNet: MR2919207
Digital Object Identifier: 10.1214/11-AIHP433

Subjects:
Primary: 62G07 , 62G20

Keywords: Empirical characteristic function , empirical process , Fourier inversion , Lévy density , Lévy process , maximal inequality , Mean square error

Rights: Copyright © 2012 Institut Henri Poincaré

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Vol.48 • No. 1 • February 2012
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