Local smoothing regression with functional data

Authors:
K. Benhenni;F. Ferraty;M. Rachdi;P. Vieu
Affiliations:
Université de Grenoble, LJK UMR CNRS 5224, Grenoble Cedex 09, France F38040;Université Paul Sabatier, LSP UMR CNRS 5583, Toulouse Cedex, France 31062;Université de Grenoble, LJK UMR CNRS 5224, Grenoble Cedex 09, France F38040;Université Paul Sabatier, LSP UMR CNRS 5583, Toulouse Cedex, France 31062
Venue:
Computational Statistics
Year:
2007

Citing 0
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Abstract

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.