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Nonparametric estimation for irregularly sampled Lévy processes

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  • Johanna Kappus

    (Universität Rostock)

Abstract

We consider nonparametric statistical inference for Lévy processes sampled irregularly, at low frequency. The estimation of the jump dynamics as well as the estimation of the distributional density are investigated. Non-asymptotic risk bounds are derived and the corresponding rates of convergence are discussed under global as well as local regularity assumptions. Moreover, minimax optimality is proved for the estimator of the jump measure. Some numerical examples are given to illustrate the practical performance of the estimation procedure.

Suggested Citation

  • Johanna Kappus, 2018. "Nonparametric estimation for irregularly sampled Lévy processes," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 141-167, April.
    • Handle: RePEc:spr:sistpr:v:21:y:2018:i:1:d:10.1007_s11203-016-9144-2
    DOI: 10.1007/s11203-016-9144-2
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    References listed on IDEAS

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    1. Kappus, Johanna, 2014. "Adaptive nonparametric estimation for Lévy processes observed at low frequency," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 730-758.
    2. Ibragimov, Rustam & Sharakhmetov, Shaturgun, 2002. "The exact constant in the Rosenthal inequality for random variables with mean zero," Scholarly Articles 2623703, Harvard University Department of Economics.
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