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II Simposio sobre Modelamiento Estadístico, Valparaiso : Chili (2010)
Classification and regression based on derivatives : a consistency result
Nathalie Villa-Vialaneix 1, 2, Fabrice Rossi 3

In some real world applications, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of derivatives is a common practice in functional data analysis, despite a lack of theoretical guarantees on the asymptotically achievable performances of a derivative based model. In this presentation, we show that a smoothing spline approach can be used to preprocess multivariate observations obtained by sampling functions on a discrete and finite sampling grid in a way that leads to a consistent scheme on the original infinite dimensional functional problem. The rate of convergence of the method is also obtained. Finally, the proposed method is tested on two real world datasets and the approach is experimentaly proven to be a good solution in the case of noisy functional predictors.
1 :  Institut de Mathématiques de Toulouse (IMT)
CNRS : UMR5219 – PRES Université de Toulouse
2 :  IUT - Département STID - Carcassonne (UPVD)
Université de Perignan Via Domitia
3 :  Laboratoire Traitement et Communication de l'Information [Paris] (LTCI)
Télécom ParisTech – CNRS : UMR5141

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