This paper is about nonparametric regression function estimation. Our estimator is a one-step projection estimator obtained by least-squares contrast minimization. The specificity of our work is to consider a new model selection procedure including a cutoff for the underlying matrix inversion, and to provide theoretical risk bounds that apply to non-compactly supported bases, a case which was specifically excluded of most previous results. Upper and lower bounds for resulting rates are provided.

中文翻译：

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回归函数估计作为部分逆问题

本文是关于非参数回归函数估计的。我们的估计器是通过最小二乘对比度最小化获得的一步投影估计器。我们工作的特殊性是考虑一个新的模型选择程序，包括基础矩阵求逆的截止值，并提供适用于非紧致支撑基础的理论风险界限，这种情况被明确排除在大多数先前的结果之外。提供了所得速率的上限和下限。