A new spatial regression estimator in the multivariate context

Dabo-Niang, Sophie; Ternynck, Camille; Yao, Anne-Francoise

doi:10.1016/j.crma.2015.04.004

Statistics

A new spatial regression estimator in the multivariate context
[Un nouvel estimateur de la fonction de régression spatiale pour données multivariées]

Présenté par : Paul Deheuvels

Dabo-Niang, Sophie ^1,² ; Ternynck, Camille ¹ ; Yao, Anne-Francoise ³

¹ Laboratoire LEM, Université Lille-3, Maison de la recherche, BP 60149, 59653 Villeneuve d'Ascq cedex, France
² MODAL team, INRIA Lille-Nord de France, France
³ Laboratoire de Mathématiques, Université Blaise-Pascal, UMR 6620, CNRS, Campus des Cézeaux, BP 80026, 63171 Aubière cedex, France

Comptes Rendus. Mathématique, Tome 353 (2015) no. 7, pp. 635-639.

Résumé
Abstract

Dans cette note, nous proposons un estimateur non paramétrique spatial de la fonction de régression $x \to r (x) : = E [Y_{i} | X_{i} = x], x \in R^{d}$ , d'un champ stationnaire ${(Y_{i}, X_{i}), i \in Z^{N}}$ de dimension $(d + 1)$ , 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 $L^{q}$ ) $(q \in N^{⁎})$ de l'estimateur à noyaux sont obtenus en considérant des processus α-mélangeants.

In this note, we propose a nonparametric spatial estimator of the regression function $x \to r (x) : = E [Y_{i} | X_{i} = x], x \in R^{d}$ , of a stationary $(d + 1)$ -dimensional spatial process ${(Y_{i}, X_{i}), i \in Z^{N}}$ , 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 $L^{q}$ norm $(q \in N^{⁎})$ of the kernel estimate are obtained when the sample considered is an α-mixing sequence.

Reçu le : 2014-01-30
Accepté le : 2015-04-03
Publié le : 2015-04-29

DOI : 10.1016/j.crma.2015.04.004

Affiliations des auteurs :

Dabo-Niang, Sophie ^{1, 2} ; Ternynck, Camille ¹ ; Yao, Anne-Francoise ³

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     author = {Dabo-Niang, Sophie and Ternynck, Camille and Yao, Anne-Francoise},
     title = {A new spatial regression estimator in the multivariate context},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {635--639},
     publisher = {Elsevier},
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     doi = {10.1016/j.crma.2015.04.004},
     language = {en},
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Dabo-Niang, Sophie; Ternynck, Camille; Yao, Anne-Francoise. A new spatial regression estimator in the multivariate context. Comptes Rendus. Mathématique, Tome 353 (2015) no. 7, pp. 635-639. doi : 10.1016/j.crma.2015.04.004. http://www.numdam.org/articles/10.1016/j.crma.2015.04.004/

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