Statistics
Admissibility results under some balanced loss functions for a functional regression model
Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 912-916.

We consider the problem of the nonparametric estimation in a functional regression model Y=r(X)+ε, with Y a real random variable response and X representing a functional variable taking values in a semi-metric space. The aim of this note is to find conditions of admissibility of Stein-type estimators of such a model under a class of balanced loss functions. Our method is to compare the risk with that obtained in the case of a quadratic loss.

On considère le problème de l'estimation non paramétrique dans un modèle de régression fonctionnelle Y=r(X)+ε, où Y est une variable aléatoire réelle et X est une variable fonctionnelle à valeurs dans un espace semi-métrique. Le but de cette note est de trouver les conditions d'admissibilité des estimateurs de type Stein de ce modèle dans une classe de fonctions de perte équilibrées. Notre méthode consiste à comparer le risque avec celui obtenu dans le cas d'une perte quadratique.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2019.10.012
Djerfi, Kouider 1; Madani, Fethi 2; Ouassou, Idir 3

1 Université Djilali Liabès de Sidi Belabbès, Algeria
2 Laboratory of Stochastic Models, Statistic and Applications, University of Tahar Moulay, Saida, Algeria
3 National School of Applied Sciences, University of Cadi Ayyad, Marrakech, Morocco
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Djerfi, Kouider; Madani, Fethi; Ouassou, Idir. Admissibility results under some balanced loss functions for a functional regression model. Comptes Rendus. Mathématique, Volume 357 (2019) no. 11-12, pp. 912-916. doi : 10.1016/j.crma.2019.10.012. http://www.numdam.org/articles/10.1016/j.crma.2019.10.012/

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