Abstract

This paper deals with the problem of the nonparametric analysis by the relative-error regression when the explanatory of a variable is of infinite dimension. Based on k-Nearest Neighbors procedure (kNN), we construct an estimator and establish its asymptotic properties. Precisely, we show its Uniform consistency in Number of Neighbors (UNN) with the precision of the convergence rate. Some empirical studies are also performed to highlight the impact of this asymptotic result in nonparametric functional statistics.

中文翻译：

---

使用函数回归器的相对误差回归的 k 个最近邻平滑

摘要

本文研究了当变量的解释为无限维时，用相对误差回归进行非参数分析的问题。基于k-最近邻过程（kNN），我们构造了一个估计器并建立了它的渐近性质。准确地说，我们展示了它在邻居数（UNN）中的一致一致性和收敛速度的精度。还进行了一些实证研究，以突出这种渐近结果对非参数泛函统计的影响。