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Improved robust model selection methods for a Lévy nonparametric regression in continuous time

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  • E. A. Pchelintsev
  • V. A. Pchelintsev
  • S. M. Pergamenshchikov

Abstract

In this paper, we develop the James–Stein improved method for the estimation problem of a nonparametric periodic function observed with Lévy noises in continuous time. An adaptive model selection procedure based on the weighted improved least squares estimates is constructed. The improvement effect for nonparametric models is studied. It turns out that in non-asymptotic setting the accuracy improvement for nonparametric models is more important than for parametric ones. Moreover, sharp oracle inequalities for the robust risks have been shown and the adaptive efficiency property for the proposed procedures has been established. The numerical simulations are given.

Suggested Citation

  • E. A. Pchelintsev & V. A. Pchelintsev & S. M. Pergamenshchikov, 2019. "Improved robust model selection methods for a Lévy nonparametric regression in continuous time," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(3), pages 612-628, July.
    • Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:612-628
    DOI: 10.1080/10485252.2019.1609672
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    Cited by:

    1. Evgeny Pchelintsev & Serguei Pergamenshchikov & Maria Leshchinskaya, 2022. "Improved estimation method for high dimension semimartingale regression models based on discrete data," Statistical Inference for Stochastic Processes, Springer, vol. 25(3), pages 537-576, October.
    2. Evgeny Pchelintsev & Serguei Pergamenshchikov & Maria Povzun, 2022. "Efficient estimation methods for non-Gaussian regression models in continuous time," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 113-142, February.

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