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Comptes Rendus Mathématique
Volume 348, n° 15-16
pages 931-934 (août 2010)
Doi : 10.1016/j.crma.2010.06.013
Received : 14 May 2010 ;  accepted : 21 June 2010
Estimation locale linéaire de la densité conditionnelle pour des données fonctionnelles
Local linear estimation of the conditional density for functional data
 

Jacques Demongeot a , Ali Laksaci b , Fethi Madani a , Mustapha Rachdi c
a Laboratoire TIMC-IMAG, UMR CNRS 5525, équipe AGIM3, faculté de médecine de Grenoble, université J. Fourier, 38700, La Tronche, France 
b Université Djillali-Liabès, BP. 89, Sidi Bel-Abbès 22000, Algérie 
c Laboratoire TIMC-IMAG, UMR CNRS 5525, équipe AGIM3, université P. Mendès France de Grenoble, UFR SHS, BP. 47, 38040 Grenoble cedex 09, France 

Résumé

Dans cette Note, nous introduisons l'estimation locale linéaire de la densité conditionnelle, quand la réponse est scalaire et la variable explicative est à valeurs dans un espace semi-métrique. Sous certaines conditions, nous établissons les convergences presque-complètes ponctuelle et uniforme, et nous donnons également les vitesses de convergence correspondantes. De plus, comme application, nous utilisons les résultats obtenus pour donner quelques propriétés asymptotiques de l'estimateur local linéaire du mode conditionnel.

The full text of this article is available in PDF format.
Abstract

In this Note, we introduce the local linear estimation of the conditional density of a scalar response variable given a random variable taking values in a semi-metric space. Under some general conditions, we establish the pointwise and uniform almost complete convergences with rates of this estimator. Moreover, as an application, we use the obtained results to derive some asymptotic properties for the local linear estimator of the conditional mode.

The full text of this article is available in PDF format.


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