Nonparametric estimation for Lévy processes from low-frequency observations - Mathematics > Statistics TheoryReport as inadecuate




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Abstract: We suppose that a L\-evy process is observed at discrete time points. Arather general construction of minimum-distance estimators is shown to giveconsistent estimators of the L\-evy-Khinchine characteristics as the number ofobservations tends to infinity, keeping the observation distance fixed. For aspecific $C^2$-criterion this estimator is rate-optimal. The connection withdeconvolution and inverse problems is explained. A key step in the proof is auniform control on the deviations of the empirical characteristic function onthe whole real line.



Author: Michael H. Neumann, Markus Reiss

Source: https://arxiv.org/







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