Communications - Scientific Letters of the University of Zilina 2018, 20(1):73-77 | DOI: 10.26552/com.C.2018.1.73-77

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

Evgeny Pchelintsev1, Valeriy Pchelintsev2, Serguei Pergamenshchikov3
1 Department of Information Technologies and Business Analytics, Tomsk State University, Russia
2 Department of Mathematics and Informatics, Tomsk Polytechnic University, Russia
3 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

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.

Keywords: improved non-asymptotic estimation; weighted least squares estimates; robust quadratic risk; non-parametric regression; Levy process; model selection; sharp oracle inequality; asymptotic efficiency

Published: March 31, 2018  Show citation

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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. doi: 10.26552/com.C.2018.1.73-77
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