Model selection method for efficient signals processing from discrete data

Abstract

The paper considers the problem of robust adaptive efficient estimating of a periodic signal modeled by a continuous time regression model with the dependent noises given by a non-Gaussian Ornstein-Uhlenbeck process with Levy subordinator in the case when continuous observation cannot be provided and only discrete time measurements are available. Adaptive model selection procedure, based on the improved weighted least square estimates, is proposed. Under some conditions on the noise distribution, sharp oracle inequality for the robust risk has been proved and the robust efficiency of the model selection procedure has been established. The numerical analysis results are given.