• Bernoulli
  • Volume 15, Number 1 (2009), 223-248.

Nonparametric estimation for Lévy processes from low-frequency observations

Michael H. Neumann and Markus Reiß

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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.

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Bernoulli, Volume 15, Number 1 (2009), 223-248.

First available in Project Euclid: 3 February 2009

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deconvolution density estimation Lévy–Khinchine characteristics minimum distance estimator


Neumann, Michael H.; Reiß, Markus. Nonparametric estimation for Lévy processes from low-frequency observations. Bernoulli 15 (2009), no. 1, 223--248. doi:10.3150/08-BEJ148.

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