Sequential model selection method for nonparametric autoregression. Issue 4 (2nd October 2019)

• Record Type: Journal Article
• Authors: Arkoun, Ouerdia; Brua, Jean-Yves; Pergamenchtchikov, Serguei
• Is Part Of: Sequential analysis. Volume 38:Issue 4(2019)
• Page Start: 437
• Page End: 460
• Publication Date: 2019-10-02
• Subjects: 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; Primary 62G08 -- Secondary 62G05; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2019.1686883
• Languages: English
• ISSNs: 0747-4946

Abstract

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.