Nonparametric regression for functional data: automatic smoothing parameter selection - SF&S Accéder directement au contenu
Article Dans Une Revue Journal of Statistical Planning and Inference Année : 2007

Nonparametric regression for functional data: automatic smoothing parameter selection

Résumé

We study regression estimation when the explanatory variable is functional. Nonparametric estimates of the regression operator have been recently introduced. They depend on a smoothing factor which controls its behavior, and the aim of our work is to construct some data-driven criterion for choosing this smoothing parameter. The criterion can be formulated in terms of a functional version of cross-validation ideas. Under mild assumptions on the unknown regression operator, it is seen that this rule is asymptotically optimal. As by-products of this result, we state some asymptotic equivalences for several measures of accuracy for nonparametric estimate of the regression operator. We also present general inequalities for bounding moments of random sums involving functional variables. Finally, a short simulation study is carried out to illustrate the behavior of our method for finite samples.

Dates et versions

hal-00171440 , version 1 (12-09-2007)

Identifiants

Citer

Mustapha Rachdi, Philippe Vieu. Nonparametric regression for functional data: automatic smoothing parameter selection. Journal of Statistical Planning and Inference, 2007, 137 (9), pp.2784-2801. ⟨10.1016/j.jspi.2006.10.001⟩. ⟨hal-00171440⟩
144 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More