No abstract

This paper considers the problem of improved adaptive estimating a periodic signal observed in the transmission channel with the dependent noise defined by semi-Markov processes with unknown probabilities and spectral characteristics. Improved adaptive model selection procedure is proposed. The comparison between improved and least squares methods is studied. Sharp oracle inequality for the procedure risk is obtained. The efficiency of the proposed procedure is established. The Monte Carlo simulation results are given.

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.