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2012 Convergence of nonparametric functional regression estimates with functional responses
Heng Lian
Electron. J. Statist. 6: 1373-1391 (2012). DOI: 10.1214/12-EJS716

Abstract

We consider nonparametric functional regression when both predictors and responses are functions. More specifically, we let $(X_{1},Y_{1}),\ldots, (X_{n},Y_{n})$ be random elements in $\mathcal{F}\times\mathcal{H}$ where $\mathcal{F}$ is a semi-metric space and $\mathcal{H}$ is a separable Hilbert space. Based on a recently introduced notion of weak dependence for functional data, we showed the almost sure convergence rates of both the Nadaraya-Watson estimator and the nearest neighbor estimator, in a unified manner. Several factors, including functional nature of the responses, the assumptions on the functional variables using the Orlicz norm and the desired generality on weakly dependent data, make the theoretical investigations more challenging and interesting.

Citation

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Heng Lian. "Convergence of nonparametric functional regression estimates with functional responses." Electron. J. Statist. 6 1373 - 1391, 2012. https://doi.org/10.1214/12-EJS716

Information

Published: 2012
First available in Project Euclid: 26 July 2012

zbMATH: 1295.62042
MathSciNet: MR2988451
Digital Object Identifier: 10.1214/12-EJS716

Subjects:
Primary: 60G10 , 62G08

Keywords: Bernstein’s inequality for martingale differences , Nadaraya-Watson estimate , nearest neighbor estimate , nonparametric functional regression , Orlicz norm

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

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