Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - University of Rouen Normandy

We consider the robust adaptive non parametric estimation problem for the periodic function observed in the continuous time regression model with the Lévy noises. We propose an adaptive model selection procedure, based on the improved weighted least square estimates. Under some conditions on the noise distribution we prove sharp oracle inequalities for the robust risks and we establish the efficiency property for the proposed model selection procedure in the adaptive setting.