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In this article we consider the nonparametric robust estimation problem forregression models in continuous time with semi-Markov noises observed indiscrete time moments. An adaptive model selection procedure is proposed. Asharp non-asymptotic oracle inequality for the robust risks is obtained. Weobtain sufficient conditions on the frequency observations under which therobust efficiency is shown. It turns out that for the semi-Markov models therobust minimax convergence rate may be faster or slower than the classical one.

Robust adaptive efficient estimation for a semi-Markov continuous time regression from discrete data