Nonparametric estimation for Lévy processes from low-frequency observations

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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 $C^2$-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.
24 pages, 2 figures

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Statistics Theory, Probability, Methodology, 62G15; 62M15

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http://salesiana.dossiersoluciones.com/handle/123456789/161738

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0709.2007
 http://arxiv.org/abs/0709.2007

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arXiv