Advances in Decision Sciences
Volume 2011 (2011), Article ID 462157, 35 pages
http://dx.doi.org/10.1155/2011/462157
Research Article

Asymptotic Normality of a Nonparametric Conditional Quantile Estimator for Random Fields

Sidi Ali Ould Abdi,1 Sophie Dabo-Niang,2 Aliou Diop,1 and Ahmedoune Ould Abdi1

1Laboratoire LERSTAD, Universitรฉ Gaston Berger, BP 234, Saint-Louis, Senegal
2Laboratoire EQUIPPE, Universitรฉ Charles De Gaulle, Lille 3, Maison de la Recherche, Domaine du Pont de Bois, BP 60149, 59653 Villeneuve d'Ascq Cedex, France

Received 16 August 2011; Revised 4 November 2011; Accepted 6 November 2011

Academic Editor: C. D. Lai

Copyright © 2011 Sidi Ali Ould Abdi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Given a stationary multidimensional spatial process ( ๐‘ i = ( ๐‘‹ i , ๐‘Œ i ) โˆˆ โ„ ๐‘‘ ร— โ„ , i โˆˆ โ„ค ๐‘ ) , we investigate a kernel estimate of the spatial conditional quantile function of the response variable ๐‘Œ i given the explicative variable ๐‘‹ i . Asymptotic normality of the kernel estimate is obtained when the sample considered is an ๐›ผ -mixing sequence.