Local smoothing regression with functional data

Karim Benhenni (1) , Frédéric Ferraty (2) , Mustapha Rachdi (3) , Philippe Vieu (2)

1 MS3 - Méthodologie Statistique et Sciences Sociales
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 SFS - Statistique Fonctionnelle & Sondages

Kernel estimates of a regression operator are investigated when the explanatory variable is of functional type. The bandwidths are locally chosen by a data-driven method based on the minimization of a functional version of a cross-validated criterion. A short asymptotic theoretical support is provided and the main body of this paper is devoted to various finite sample size applications. In particular, it is shown through some simulations, that a local bandwidth choice enables to capture some underlying heterogeneous structures in the functional dataset. As a consequence, the estimation of the relationship between a functional variable and a scalar response, and hence the prediction, can be significantly improved by using local smoothing parameter selection rather than global one. This is also confirmed from a chemometrical real functional dataset. These improvements are much more important than in standard finite dimensional setting.

Mots clés: Regression operator; Local versus global bandwidths; Functional data; Cross-validation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Karim Benhenni, Frédéric Ferraty, Mustapha Rachdi, Philippe Vieu. Local smoothing regression with functional data. Computational Statistics, 2007, 22 (3), pp.353-369. ⟨10.1007/s00180-007-0045-0⟩. ⟨hal-00795596⟩