Nonparametric estimation for Lévy processes from low-frequency observations

Details Nonparametric estimation for Lévy processes from low-frequency observations Nonparametric estimation for Lévy processes from low-frequency observations

2007-09-13

arxiv.org/abs/0709.2007v2

Mathematics

Statistics Theory

24 pages, 2 figures

Scientific paper

We suppose that a L\'evy process is observed at discrete time points. A rather general construction of minimum-distance estimators is shown to give consistent estimators of the L\'evy-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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