Sequential model selection method for nonparametric autoregression. Issue 4 (2nd October 2019) - Arkoun, Ouerdia; Brua, Jean-Yves; Pergamenchtchikov, Serguei
Abstract: In 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.