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

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

Research output: Contribution to journalArticle


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.

Original languageEnglish
JournalJournal of Nonparametric Statistics
Publication statusPublished - 1 Jan 2019



  • 62G05
  • 62G08
  • adaptive estimation
  • asymptotic efficiency
  • Improved non-asymptotic estimation
  • James–Stein procedures
  • Lévy process
  • model selection
  • nonparametric regression
  • robust quadratic risk
  • sharp oracle inequality

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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