Classification and regression based on derivatives : a consistency result

Abstract : 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.
Type de document :
Communication dans un congrès
II Simposio sobre Modelamiento Estadístico, Dec 2010, Valparaiso, Chile
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https://hal.archives-ouvertes.fr/hal-00668212
Contributeur : Nathalie Villa-Vialaneix <>
Soumis le : jeudi 9 février 2012 - 13:07:48
Dernière modification le : jeudi 9 février 2017 - 15:18:24
Document(s) archivé(s) le : jeudi 22 novembre 2012 - 11:50:29

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  • HAL Id : hal-00668212, version 1

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Nathalie Villa-Vialaneix, Fabrice Rossi. Classification and regression based on derivatives : a consistency result. II Simposio sobre Modelamiento Estadístico, Dec 2010, Valparaiso, Chile. <hal-00668212>

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