Advances on nonparametric regression for functional variables

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

1 LSP - Laboratoire de Statistique et Probabilités
2 IMAG - Institut Montpelliérain Alexander Grothendieck

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.

Mots clés: Functional Data; Asymptotic Studies; Regression; Nonparametric Model; Wild Functional Bootstrap; Wild Functional Bootstrap.

Domaines: Statistiques [math.ST]

Frédéric Ferraty, Andre Mas, Philippe Vieu. Advances on nonparametric regression for functional variables. Australian and New Zealand Journal of Statistics, 2007, 49 (3), pp.267-286. ⟨10.1111/j.1467-842X.2007.00480.x⟩. ⟨hal-00635687v2⟩