Recursive estimation of nonparametric regression with functional covariate.

Aboubacar Amiri; Christophe Crambes; Baba Thiam

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Recursive estimation of nonparametric regression with functional covariate.

Working paper

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Recursive estimation of nonparametric regression with functional covariate.

Aboubacar Amiri, Christophe Crambes and Baba Thiam

Abstract

asymptotic normality

Functional data

recursive kernel estimators

regression function

quadratic error

almost sure convergence

asymptotic normality.

62G05, , 62G07, 62G08.

The main purpose of this work is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of recursive kernel estimates of the regression function are derived. These results are established with rates and precise evaluation of the constant terms. Also, a central limit theorem for this class of estimators is established. The method is evaluated on simulations and a real data set study.

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Title: Recursive estimation of nonparametric regression with functional covariate.
Creators - without role: Aboubacar Amiri - Economie Quantitative, Intégration, Politiques Publiques et Econométrie
Christophe Crambes - Université de Montpellier, Institut Montpelliérain Alexander Grothendieck - IMAG
Baba Thiam - Economie Quantitative, Intégration, Politiques Publiques et Econométrie
Identifiers: 9943764709311
Academic Unit: Institut Montpelliérain Alexander Grothendieck - IMAG
Language: English
Resource Type: Working paper
Local Fields: hal-00750894