Improved estimation of a regression function with the Levy noise from discrete data
Salle des séminaires, M.0.1
Tomsk State University
We consider the problem of estimating function in a periodic regression in continuous time with the Levy noise by discrete time observations. We use the model selection approach and develop a new adaptive procedure, which involves special modifications of the well-known James-Stein estimates, to improve the accuracy of the basic weighted least square estimates. The sharp oracle inequalities for the risks have been obtained and the asymptotic efficiency of the procedure has been proved. The numerical simulation results are given.