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Admissibility results under some balanced loss functions for a functional regression model. (Résultats d’admissibilité dans une classe de fonctions de perte équilibrées dans un modèle de régression fonctionnelle.) (English. French summary) Zbl 1434.62043

Summary: We consider the problem of the nonparametric estimation in a functional regression model \(Y = r(X) + \varepsilon \), 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.

MSC:

62G07 Density estimation
62G08 Nonparametric regression and quantile regression
62H12 Estimation in multivariate analysis

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