Nonparametric local polynomial regression for functional covariates

Fuente: arXiv
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Autores principales: Jirak, Moritz, Kneip, Alois, Meister, Alexander, Pahl, Mario
Formato: Preprint
Publicado: 2025
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author Jirak, Moritz
Kneip, Alois
Meister, Alexander
Pahl, Mario
author_facet Jirak, Moritz
Kneip, Alois
Meister, Alexander
Pahl, Mario
contents We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters remain to be selected. We provide a general asymptotic upper bound on the estimation error and show that this procedure achieves polynomial convergence rates under appropriate tuning and supersmoothness of the regression function. Such polynomial convergence rates have usually been considered to be non-attainable in nonparametric functional regression without any additional strong structural constraints such as linearity of the regression function.
format Preprint
id arxiv_https___arxiv_org_abs_2504_05819
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Nonparametric local polynomial regression for functional covariates
Jirak, Moritz
Kneip, Alois
Meister, Alexander
Pahl, Mario
Statistics Theory
62R10, 62G08
We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters remain to be selected. We provide a general asymptotic upper bound on the estimation error and show that this procedure achieves polynomial convergence rates under appropriate tuning and supersmoothness of the regression function. Such polynomial convergence rates have usually been considered to be non-attainable in nonparametric functional regression without any additional strong structural constraints such as linearity of the regression function.
title Nonparametric local polynomial regression for functional covariates
topic Statistics Theory
62R10, 62G08
url https://arxiv.org/abs/2504.05819