Nonparametric adaptive estimation for pure jump Lévy processes

F. Comte; V. Genon-Catalot

Annales de l'I.H.P. Probabilités et statistiques (2010)

  • Volume: 46, Issue: 3, page 595-617
  • ISSN: 0246-0203

Abstract

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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 n 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 estimator. The risk bound for the adaptive estimator is obtained under additional assumptions on the Lévy density. Examples of models fitting in our framework are described and rates of convergence of the estimator are discussed.

How to cite

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Comte, F., and Genon-Catalot, V.. "Nonparametric adaptive estimation for pure jump Lévy processes." Annales de l'I.H.P. Probabilités et statistiques 46.3 (2010): 595-617. <http://eudml.org/doc/241006>.

@article{Comte2010,
abstract = {This paper is concerned with nonparametric estimation of the Lévy density of a pure jump Lévy process. The sample path is observed at n 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 estimator. The risk bound for the adaptive estimator is obtained under additional assumptions on the Lévy density. Examples of models fitting in our framework are described and rates of convergence of the estimator are discussed.},
author = {Comte, F., Genon-Catalot, V.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {adaptive estimation; deconvolution; Lévy process; nonparametric projection estimator},
language = {eng},
number = {3},
pages = {595-617},
publisher = {Gauthier-Villars},
title = {Nonparametric adaptive estimation for pure jump Lévy processes},
url = {http://eudml.org/doc/241006},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Comte, F.
AU - Genon-Catalot, V.
TI - Nonparametric adaptive estimation for pure jump Lévy processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2010
PB - Gauthier-Villars
VL - 46
IS - 3
SP - 595
EP - 617
AB - This paper is concerned with nonparametric estimation of the Lévy density of a pure jump Lévy process. The sample path is observed at n 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 estimator. The risk bound for the adaptive estimator is obtained under additional assumptions on the Lévy density. Examples of models fitting in our framework are described and rates of convergence of the estimator are discussed.
LA - eng
KW - adaptive estimation; deconvolution; Lévy process; nonparametric projection estimator
UR - http://eudml.org/doc/241006
ER -

References

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