Statistique
Estimation non paramétrique de quantiles conditionnels pour des variables fonctionnelles spatialement dépendantes
[Nonparametric estimation of conditional quantiles for functional and spatial dependent variables]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1075-1080.

Consider Zi=(Xi,Yi), iNN be a F×R-valued measurable strictly stationary spatial process, where F is a semi-metric space. We study a kernel estimator of conditional quantiles of the univariate response variable Yi given the functional variable Xi. The main aim of this Note is to prove the almost complete convergence (with rate) of this estimate.

Étant donné un champ aléatoire fonctionnel, stationnaire (Zi=(Xi,Yi),iNN, N>0) à valeurs dans F×R, où F est un espace semi-métrique, de dimension éventuellement infinie. Dans cette Note, on se propose d'étudier la covariation spatiale des deux variables Xi et Yi via l'estimation non paramétrique des quantiles conditionnels de Yi sachant Xi. Nous construisons un estimateur à noyau pour ce modèle non paramétrique spatial et nous établissons sa vitesse de convergence presque complètement.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.06.012
Laksaci, Ali 1; Maref, Fouzia 2

1 Laboratoire de mathématiques, université Djilali-Liabes, BP 89, Sidi Bel Abbes, 22000, Algérie
2 Université de Saida, Saida, 20000, Algérie
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Laksaci, Ali; Maref, Fouzia. Estimation non paramétrique de quantiles conditionnels pour des variables fonctionnelles spatialement dépendantes. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1075-1080. doi : 10.1016/j.crma.2009.06.012. http://www.numdam.org/articles/10.1016/j.crma.2009.06.012/

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