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Theses

Modèles de régression linéaire pour variables explicatives fonctionnelles

Abstract : Functional data analysis is a branch of statistics which has highly developed these last years. In this thesis, we are interested in functional regression problems in which we want to explain the variations of a real interest variable from the variations of a functional covariate, that is to say a variable taking its values in an infinite dimensional space. We consider more particularly linear regression models. Two kinds of estimation are proposed: the estimation of conditional quantiles and the estimation of the conditional mean (for which we consider the case where the covariate is non-noisy, and then when there are measurement errors). In each case, estimators based on spline functions are proposed, solutions of penalized minimization problems, the penalization being introduced to circumvent the problem of the infinite dimension. Finally, we are interested in the practical aspects of this study, by the maen of simulations, then on a real data set concerning the prediction of ozone pollution peaks in the city of Toulouse.
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https://tel.archives-ouvertes.fr/tel-00134003
Contributor : Christophe Crambes <>
Submitted on : Wednesday, February 28, 2007 - 2:20:22 PM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
Long-term archiving on: : Wednesday, April 7, 2010 - 2:52:53 AM

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  • HAL Id : tel-00134003, version 1

Citation

Christophe Crambes. Modèles de régression linéaire pour variables explicatives fonctionnelles. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2006. Français. ⟨tel-00134003⟩

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