Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - University of Rouen Normandy

We consider the adaptive robust nonparametric estimation problem for a periodic function observed in the framework of a continuous time regression model in fixed time moments with semimartingale noises. As an example, we consider the regression model with the noise defined by non-Gaussian Ornstein--Uhlenbeck processes with jumps. A model selection procedure, based on the shrinkage weighted least squares estimates, is proposed. Constructive sufficient conditions for the observations frequency are found under which sharp oracle inequalities for the robust risks are obtained. Moreover, on the basis of these inequalities the robust efficiency property has been established in adaptive setting. Finally, the numerical analysis is given which confirm the obtained theoretical results in practice.