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

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.

Keywords

• improved non-asymptotic estimation
• weighted least squares estimates
• robust quadratic risk
• non-parametric regression
• levy process
• model selection
• sharp oracle inequality
• asymptotic efficiency