Improved estimation method for high dimension semimartingale regression models based on discrete data - Pchelintsev, Evgeny A. (Statistical inference for stochastic processes)
We consider the robust adaptive nonparametric estimation problem for a periodic function observed in the framework of a continuous time regression model with semimartingale noises, i.e. by incomplete observations. As an example, we consider the regression model with noise defined by non-Gaussian Ornstein-Uhlenbeck processes. A model selection procedure, based on the shrinkage (improved) 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 Monte - Carlo simulations are given which confirm numerically the obtained theoretical results.