Robust signal processing in nonparametric autoregression

Abstract

In this paper we consider the problem of a robust adaptive estimation of a periodic signal modeled by the nonparametric autoregression. We develop a new sequential model selection method, using improved estimation approach and the efficient sequential kernel estimators. This procedure is based on the sequential estimators. For robust quadratic risk of proposed estimate we obtain sharp oracle inequality that allows us to establish the efficiency property of this model selection procedure. We give the Monte Carlo simulation results for numerical comparing of the risks of proposed improved procedure and ordinary least squares estimates.