The k nearest neighbors smoothing of the relative-error regression with functional regressor

Ibrahim M. Almanjahie, Khlood A. Aissiri, Ali Laksaci and Zouaoui Chikr Elmezouar

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 12, 4196-4209

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.

Date: 2022
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DOI: 10.1080/03610926.2020.1811870

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