Bernoulli

  • 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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 3 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.bj/1233669889

Digital Object Identifier
doi:10.3150/08-BEJ148

Mathematical Reviews number (MathSciNet)
MR2546805

Zentralblatt MATH identifier
1200.62095

Keywords
deconvolution density estimation Lévy–Khinchine characteristics minimum distance estimator

Citation

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


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