| Popis: |
We study a robust adaptive nonparametric estimation problem for periodic functions observed in discrete fixed time moments with non-Gaussian Ornstein–Uhlenbeck noises. For this problem we develop a model selection method, based on the shrinkage (improved) weighted least squares estimates. We found constructive sufficient conditions for the observations frequency under which sharp oracle inequalities for the robust risks are obtained. Moreover, on the basis of the obtained oracle inequalities we establish for the proposed model selection procedures the robust efficiency property in adaptive setting. Then, we apply the constructed model selection procedures to estimation problems in Big Data models in continuous time. Finally, we provide Monte - Carlo simulations confirming the obtained theoretical results. |
