Comptes Rendus
no. 5
Statistics
Asymptotic normality of a robust kernel estimator of the regression function for functional ergodic data: Case of an unknown scale parameter
[Normalité asymptotique de l'estimateur à noyau de la fonction de régression robuste du paramètre d'échelle pour des données fonctionnelles ergodiques : cas d'un paramètre d'échelle inconnu]

Présenté par : the Editorial Board

Mohammed Kadi Attouch1 ; Zoulikha Kaid1 ; Hayat Louhab2
1 Department of Mathematics, College of Science, King Khalid University, PO. Box 9004, Abha, Saudi Arabia
2 Université Djillali-Liabès, Laboratoire de probabilités, statistique, processus stochastiques, BP. 89, 22000 Sidi Bel-Abbès, Algeria
Comptes Rendus. Mathématique, Volume 357 (2019) no. 5, pp. 478-481.

Sous un modèle de régression non paramétrique robuste, nous considérons le problème d'estimation de la fonction de score ψx pour x fixé dans un espace fonctionnel et quand le paramètre d'échelle est inconnu. L'objectif principal est d'établir la normalité asymptotique de cet estimateur pour un processus ergodique stationnaire sans hypothèse de mélange.

Under a nonparametric robust regression model, we consider the problem of estimating the score function ψx for a fixed x in a functional space and with unknown scale parameter. The principal aim of this work is to establish the asymptotic normality of this estimator for a stationary ergodic process without any use of traditional mixing conditions.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2019.04.010
Mohammed Kadi Attouch 1 ; Zoulikha Kaid 1 ; Hayat Louhab 2

1 Department of Mathematics, College of Science, King Khalid University, PO. Box 9004, Abha, Saudi Arabia
2 Université Djillali-Liabès, Laboratoire de probabilités, statistique, processus stochastiques, BP. 89, 22000 Sidi Bel-Abbès, Algeria 
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Mohammed Kadi Attouch; Zoulikha Kaid; Hayat Louhab. Asymptotic normality of a robust kernel estimator of the regression function for functional ergodic data: Case of an unknown scale parameter. Comptes Rendus. Mathématique, Volume 357 (2019) no. 5, pp. 478-481. doi : 10.1016/j.crma.2019.04.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.04.010/

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