Non Asymptotic Sharp Oracle Inequalities for the Improved Model Selection Procedures for the Adaptive Nonparametric Signal Estimation Problem 

  • Evgeny Pchelintsev
  • Valeriy Pchelintsev
  • Serguei Pergamenshchikov
Keywords: improved non-asymptotic estimation, weighted least squares estimates, robust quadratic risk, non-parametric regression, Levy process, model selection, sharp oracle inequality, asymptotic efficiency

Abstract

In this paper, we consider the robust adaptive non parametric estimation problem for the periodic function observed with the Levy noises in continuous time. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed. Sharp oracle inequalities for the robust risks have been obtained.

Author Biographies

Evgeny Pchelintsev

Department of Information Technologies and Business Analytics, Tomsk State University, Russia

Valeriy Pchelintsev

Department of Mathematics and Informatics, Tomsk Polytechnic University, Russia

Serguei Pergamenshchikov

Laboratoire de Mathematiques Raphael Salem, Universite de Rouen, Saint Etienne du Rouvray, France and International Laboratory of Statistics of Stochastic Processes and Quantitative Finance of Tomsk State University, Russia

Published
2018-03-31
How to Cite
Pchelintsev, E., Pchelintsev, V., & Pergamenshchikov, S. (2018). Non Asymptotic Sharp Oracle Inequalities for the Improved Model Selection Procedures for the Adaptive Nonparametric Signal Estimation Problem . Communications - Scientific Letters of the University of Zilina, 20(1), 73-77. Retrieved from http://journals.uniza.sk/index.php/communications/article/view/49
Issue
Vol 20 No 1 (2018)
Section
Articles