Adaptive Robust Efficient Methods for Periodic Signal Processing Observed with Colours Noises

Abstract

In this paper, we consider the problem of robust adaptive efficient estimating a periodic signal observed in the transmission channel with the dependent noise defined by non-Gaussian Ornstein-Uhlenbeck processes with unknown correlation properties. Adaptive model selection procedures, based on the shrinkage weighted least squares estimates, are proposed. The comparison between shrinkage and least squares methods is studied and the advantages of the shrinkage methods are analyzed. Estimation properties for proposed statistical algorithms are studied on the basis of the robust mean square accuracy defined as the maximum mean square estimation error over all possible values of unknown noise parameters. Sharp oracle inequalities for the robust risks have been obtained. The robust efficiency of the model selection procedure has been established.

Keywords

• asymptotic efficiency
• model selection
• non-parametric regression
• ornstein-uhlenbeck process
• periodic signals
• robust quadratic risk
• sharp oracle inequality
• shrinkage estimation
• weighted least squares estimates.