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Note on conditional quantiles for functional ergodic data
[Note sur les quantiles conditionnels pour variables fonctionnelles ergodiques]

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Benziadi, Fatima1 ; Laksaci, Ali2 ; Tebboune, Fethallah3
1 Université Moulay Taher de Saida, Algeria
2 Laboratoire Statistique et Processus stochastiques, Université Djillali-Liabès, BP 89, S. B. A. 22000, Algeria
3 Université Djillali-Liabes, Sidi Bel Abbès, Algeria
Comptes Rendus. Mathématique, Tome 354 (2016) no. 6, pp. 628-633.

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In this Note, we study the recursive kernel estimator of the conditional quantile of a scalar response variable Y given a random variable (rv) X taking values in a semi-metric space. We establish the almost complete consistency of this estimate when the observations are sampled from a functional ergodic process.

Dans cette Note, nous étudions l'estimateur à noyau récursif des quantiles conditionnels d'une variable réponse réelle Y sachant une variable aléatoire fonctionnelle X. Nous établissons la convergence presque complète de cet estimateur estimation lorsque les observations ont une corrélation ergodique.

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Accepté le :
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DOI : 10.1016/j.crma.2016.03.005

Benziadi, Fatima 1 ; Laksaci, Ali 2 ; Tebboune, Fethallah 3

1 Université Moulay Taher de Saida, Algeria
2 Laboratoire Statistique et Processus stochastiques, Université Djillali-Liabès, BP 89, S. B. A. 22000, Algeria
3 Université Djillali-Liabes, Sidi Bel Abbès, Algeria 
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Benziadi, Fatima; Laksaci, Ali; Tebboune, Fethallah. Note on conditional quantiles for functional ergodic data. Comptes Rendus. Mathématique, Tome 354 (2016) no. 6, pp. 628-633. doi : 10.1016/j.crma.2016.03.005. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2016.03.005/

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