Quantile regression when the covariates are functions

Hervé Cardot (1) , Christophe Crambes (2) , Pascal Sarda (2)

1 CESAER - Centre d'Economie et de Sociologie Rurales Appliquées à l'Agriculture et aux Espaces Ruraux
2 LSP - Laboratoire de Statistique et Probabilités

This paper deals with a linear model of regression on quantiles when the explanatory variable takes values in some functional space and the response is scalar. We propose a spline estimator of the functional coefficient that minimizes a penalized L1 type criterion. Then, we study the asymptotic behavior of this estimator. The penalization is of primary importance to get existence and convergence.

Mots clés: analyse de données fonctionnelles; quantiles conditionnels; fonctions splines; pénalisation

Domaines: Statistiques [math.ST]

Hervé Cardot, Christophe Crambes, Pascal Sarda. Quantile regression when the covariates are functions. Journal of Nonparametric Statistics, 2005, 17, pp.841-856. ⟨hal-00134226⟩