- Volume 15, Number 1 (2009), 223-248.
Nonparametric estimation for Lévy processes from low-frequency observations
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.
Bernoulli, Volume 15, Number 1 (2009), 223-248.
First available in Project Euclid: 3 February 2009
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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. https://projecteuclid.org/euclid.bj/1233669889