Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

We study a high dimension semimartingale regression model observed in the discrete time moments in a nonparametric setting. Improved (shrinkage) estimation methods are developed and the non-asymptotic comparison between shrinkage and least squares estimates is studied. Then, a model selection method based on these estimates is developed. Non-asymptotic sharp oracle inequalities for the constructed model selection procedure are obtained. Constructive sufficient conditions for the observation frequency providing the robust efficiency property in adaptive setting are found.