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.

中文翻译：

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非参数自回归的序列模型选择方法

摘要 本文考虑了二次风险的非参数自回归估计问题。为此，我们基于 Arkoun 和 Pergamenshchikov (2016) 提出的高效序列核估计器开发了一种新的自适应序列模型选择方法。此外，我们为一般回归模型开发了一种新的分析工具，以获得通常二次和稳健二次风险的非渐近尖锐预言不等式。然后，我们证明构建的序列模型选择程序在预言机不等式的意义上是最优的。