Robust adaptive efficient estimation for a semi-Markov continuous time regression from discrete data V. S. Barbu, S. Beltaief, S. M. Pergamenshchikov
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ArticleSubject(s): непрерывная регрессия | робастное оценивание | регрессионные модели | оракульные неравенства | полумарковские моделиGenre/Form: статьи в журналах Online resources: Click here to access online
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Теория вероятностей и ее применения Т. 64, № 1. С. 156-157Abstract: In this article we consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises observed in discrete time moments. An adaptive model selection procedure is proposed. A sharp non-asymptotic oracle inequality for the robust risks is obtained. We obtain sufficient conditions on the frequency observations under which the robust efficiency is shown. It turns out that for the semi-Markov models the robust minimax convergence rate may be faster or slower than the classical one.
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In this article we consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises observed in discrete time moments. An adaptive model selection procedure is proposed. A sharp non-asymptotic oracle inequality for the robust risks is obtained. We obtain sufficient conditions on the frequency observations under which the robust efficiency is shown. It turns out that for the semi-Markov models the robust minimax convergence rate may be faster or slower than the classical one.
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