Sequential Model Selection Method for Nonparametric Autoregression

TL;DR

This paper introduces a novel adaptive sequential model selection method for nonparametric autoregression estimation, providing sharp oracle inequalities and demonstrating optimality in risk assessment.

Contribution

It develops a new sequential model selection approach for nonparametric autoregression and introduces an analytical tool for sharp risk inequalities.

Findings

The method achieves optimal risk bounds.

It provides non-asymptotic sharp oracle inequalities.

The approach is applicable to general regression models.

Abstract

In this paper for the first time the nonparametric autoregression estimation problem for the 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 or- acle inequalities for both usual quadratic and robust quadratic risks. Then, we show that the constructed sequential model selection proce- dure is optimal in the sense of oracle inequalities.