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Comptes Rendus Mathématique
Volume 353, n° 7
pages 635-639 (juillet 2015)
Doi : 10.1016/j.crma.2015.04.004
Received : 30 January 2014 ;  accepted : 3 April 2015
A new spatial regression estimator in the multivariate context
Un nouvel estimateur de la fonction de régression spatiale pour données multivariées
 

Sophie Dabo-Niang a, c , Camille Ternynck a , Anne-Francoise Yao b
a Laboratoire LEM, Université Lille-3, Maison de la recherche, BP 60149, 59653 Villeneuve d'Ascq cedex, France 
b Laboratoire de Mathématiques, Université Blaise-Pascal, UMR 6620, CNRS, Campus des Cézeaux, BP 80026, 63171 Aubière cedex, France 
c MODAL team, INRIA Lille-Nord de France, France 

Abstract

In this note, we propose a nonparametric spatial estimator of the regression function  , of a stationary  -dimensional spatial process  , at a point located at some station j. The proposed estimator depends on two kernels in order to control both the distance between observations and the spatial locations. Almost complete convergence and consistency in   norm   of the kernel estimate are obtained when the sample considered is an α -mixing sequence.

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Résumé

Dans cette note, nous proposons un estimateur non paramétrique spatial de la fonction de régression  , d'un champ stationnaire   de dimension  , à un point localisé à un site donné j. L'estimateur proposé est composé de deux noyaux permettant de contrôler à la fois la distance entre les observations et entre les sites. La convergence presque complète ainsi que la convergence en moyenne d'ordre q (norme  )   de l'estimateur à noyaux sont obtenus en considérant des processus α -mélangeants.

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