Advances on nonparametric regression for functional variables

2006/03/03 by Frédéric Ferraty, Ferraty, Frédéric, André Mas +3
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.math/0603084

openalex publication_date 2006/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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