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Sequential model selection method for nonparametric autoregression |
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| Authors: | Ouerdia Arkoun Jean-Yves Brua Serguei Pergamenchtchikov |
| Affiliation: | 1. Sup'Biotech, Laboratoire BIRL, Villejuif, France;2. Normandie Université, Université de Rouen, Laboratoire de Mathématiques Rapha?l Salem, Saint-Etienne du Rouvray, France;3. Ouerdia.Arkoun@supbiotech.fr;5. Normandie Université, Université de Rouen, Laboratoire de Mathématiques Rapha?l Salem, Saint-Etienne du Rouvray, France;6. International Laboratory of Statistics of Stochastic Processes and Quantitative Finance, National Research Tomsk State University, Tomsk, Russian Federation |
| Abstract: | AbstractIn this article, the nonparametric autoregression estimation problem for quadratic risks is considered. To this end, we develop a new adaptive sequential model selection method based on the efficient sequential kernel estimators proposed by Arkoun and Pergamenshchikov (2016). Moreover, we develop a new analytical tool for general regression models to obtain the non-asymptotic sharp oracle inequalities for both usual quadratic and robust quadratic risks. Then, we show that the constructed sequential model selection procedure is optimal in the sense of oracle inequalities. |
| Keywords: | Model selection nonasymptotic estimation nonparametric autoregression nonparametric estimation robust risk sharp oracle inequalitiesModel selection nonasymptotic estimation nonparametric autoregression nonparametric estimation robust risk sharp oracle inequalities |