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Comptes Rendus Mathématique
Volume 339, n° 2
pages 141-144 (juillet 2004)
Doi : 10.1016/j.crma.2004.04.016
Received : 13 November 2003 ;  accepted : 15 April 2004
Estimation spline de quantiles conditionnels pour variables explicatives fonctionnelles
Spline estimation of conditional quantiles for functional covariates

Hervé  Cardot a ,  Christophe  Crambes b ,  Pascal  Sarda bc
aUnité biométrie et intelligence artificielle, INRA, Toulouse, BP 27, 31326 Castanet-Tolosan cedex, France 
bLaboratoire de statistique et probabilités, UMR CNRS C5583, université Paul Sabatier, 31062 Toulouse cedex, France 
cGRIMM, EA 3686, université Toulouse-le-Mirail, 31058 Toulouse cedex, France 

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Cette Note a pour objet un modèle linéaire de régression linéaire sur quantiles lorsque la variable explicative est à valeurs dans un espace fonctionnel alors que la variable réponse est réelle. Nous proposons un estimateur spline du coefficient fonctionnel basé sur la minimisation d'un critère de type   pénalisé (la pénalisation est primordiale pour avoir l'existence et la convergence de l'estimateur), puis nous étudions le comportement asymptotique de cet estimateur. Pour citer cet article : H. Cardot et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).

Abstract

This Note deals with a linear model of regression on quantiles with the explanatory variable taking values in some functional space and a scalar response. We propose a spline estimator of the functional coefficient that minimizes a penalized   type criterion (the penalization is of primary importance to get existence and convergence of the estimator), then we study the asymptotic behaviour of this estimator. To cite this article: H. Cardot et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).




© 2004  Académie des sciences@@#104156@@

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