Généralités sur l’estimateur de type Stein de l’opérateur de régression pour des données fonctionnelles
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Date
2020-03-05
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Abstract
Résumé (Français et/ou Anglais) :
The main question raised in this thesis is the improvement of the usual estimator for a nonparametric functional regression model (fixed design), under a non-quadratic loss function. Our contribution on this subjectis the proposal of some classes of loss functions generalizing that proposed by Zellner (balanced loss function). Therefore, we show that the usual estimator (the kernel estimator in this case) is:
1- Inadmissible for some classes of these balanced loss functions, hence the possibility to improve it by shrinkage. This is realized in the case of loss functions : quadratic balanced loss, weighted quadratic balanced loss, Linex balanced loss.
2- Admissible in some cases, particularly for loss functions : balanced logistic loss, reflected normal balanced loss, absolute balanced losswith1/2 <ω< 1. This is a phenomenon that occurs independently of the dimension, contrary to on whatwasrecognized the Stein phenomenon.
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Doctorat en Sciences
