We suppose that a Lévy process is observed at discrete time points. A rather general construction of minimum-distance estimators is shown to give consistent estimators of the Lévy–Khinchine characteristics as the number of observations tends to infinity, keeping the observation distance fixed. For a specific C2-criterion this estimator is rate-optimal. The connection with deconvolution and inverse problems is explained. A key step in the proof is a uniform control on the deviations of the empirical characteristic function on the whole real line.
Publié le : 2009-02-15
Classification:
deconvolution,
density estimation,
Lévy–Khinchine characteristics,
minimum distance estimator
@article{1233669889,
author = {Neumann, Michael H. and Rei\ss , Markus},
title = {Nonparametric estimation for L\'evy processes from low-frequency observations},
journal = {Bernoulli},
volume = {15},
number = {1},
year = {2009},
pages = { 223-248},
language = {en},
url = {http://dml.mathdoc.fr/item/1233669889}
}
Neumann, Michael H.; Reiß, Markus. Nonparametric estimation for Lévy processes from low-frequency observations. Bernoulli, Tome 15 (2009) no. 1, pp. 223-248. http://gdmltest.u-ga.fr/item/1233669889/