Estimation non paramétrique du mode conditionnel pour variable explicative fonctionnelle

Sophie Dabo-Niang; Ali Laksaci

doi:10.1016/j.crma.2006.11.022

Statistique/Probabilités

Estimation non paramétrique du mode conditionnel pour variable explicative fonctionnelle

Présenté par : Paul Deheuvels

Sophie Dabo-Niang ¹ ; Ali Laksaci ²

¹ Laboratoire GREMARS, maison de la recherche, Université Lille 3, BP 60149, 59653 Villeneuve d'Ascq cedex, France
² Laboratoire de mathématique, Université Djillali Liabes, Sidi Bel Abbès, Algèrie

Comptes Rendus. Mathématique, Volume 344 (2007) no. 1, pp. 49-52.

Résumé
Abstract

Nous étudions l'estimateur à noyau du mode de la distribution d'une variable réelle Y conditionnellement à une variable explicative X, à valeurs dans un espace semi-métrique. Nous établissons la convergence en norme $L^{p}$ de l'estimateur. Les résultats asymptotiques établis sont liés aux probabilités de petites boules de la loi de la variable explicative et aussi à la régularité de la densité conditionnelle. Nos conditions et résultats unifient les deux cadres des variables explicatives de dimensions finie et infinie.

We study a kernel estimator of the conditional mode of a scalar response variable Y given a random variable X taking values in a semi-metric space. We establish the consistency in $L^{p}$ norm of the estimator. The asymptotic results are closely related to the concentration properties on small balls of the probability measure of the underlying explanatory variable and the regularity of the conditional density. Our conditions and results unify both cases of finite and infinite dimensional regressors.

Reçu le : 2005-08-25
Accepté le : 2006-10-24
Publié le : 2006-12-15

DOI : 10.1016/j.crma.2006.11.022

Affiliations des auteurs :

Sophie Dabo-Niang ¹ ; Ali Laksaci ²

¹ Laboratoire GREMARS, maison de la recherche, Université Lille 3, BP 60149, 59653 Villeneuve d'Ascq cedex, France
² Laboratoire de mathématique, Université Djillali Liabes, Sidi Bel Abbès, Algèrie

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Sophie Dabo-Niang; Ali Laksaci. Estimation non paramétrique du mode conditionnel pour variable explicative fonctionnelle. Comptes Rendus. Mathématique, Volume 344 (2007) no. 1, pp. 49-52. doi : 10.1016/j.crma.2006.11.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.11.022/

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Cité par 16 documents. Sources : Crossref, zbMATH

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