Advances on nonparametric regression for functional variables

Frédéric Ferraty; Andre MAS; Philippe Vieu

hal-00020028, version 1

Advances on nonparametric regression for functional variables

Frédéric Ferraty () ¹, Andre MAS () ², Philippe Vieu () ¹

Australian and New Zealand Journal of Statistics (2007) 49 (3), 1-20

Abstract: We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is attacked by mean of nonparametric kernel approach which has been recently adapted to this functional context. We derive theoretical results by giving a deep asymptotic study of the behaviour of the estimate, including mean squared convergence (with rates and precise evaluation of the constant terms) as well as asymptotic distribution. Practical use of these results are relying on the ability to estimate these constants. Some perspectives in this direction are discussed including the presentation of a functional version of bootstrapping ideas.

1: Laboratoire de Statistiques et Probabilités (LSProba)
CNRS : UMR5583 – Université Paul Sabatier [UPS] - Toulouse III – Institut National des Sciences Appliquées (INSA) - Toulouse
2: Institut de Mathématiques et de Modélisation de Montpellier (I3M)
CNRS : UMR5149 – Université Montpellier II - Sciences et techniques

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From: André Mas <>
Submitted on: Friday, 3 March 2006 14:09:36
Updated on: Tuesday, 19 March 2013 16:01:54

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