Nonparametric estimation for irregularly sampled Lévy processes

Johanna Kappus ()
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Johanna Kappus: Universität Rostock

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 1, No 6, 167 pages

Abstract: 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.

Keywords: Nonparametric statistical inference; Lévy processes; Irregular sampling; Density estimation; 62G05; 62G07; 62G20; 62M05 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11203-016-9144-2

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