Sélection automatique du paramètre de lissage pour l'estimation non paramétrique de la régression pour des données fonctionnelles

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• 作者：Mustapha Rachdi and Philippe Vieu
• 刊名：Comptes Rendus Mathematique
• 出版年：2005
• 出版时间：2005
• 年：2005
• 卷：341
• 期：6
• 页码：365-368
• 全文大小：81 K

文摘

We study regression estimation when the explanatory variable is functional. Nonparametric estimates of the regression operator have been recently introduced. They depend on a smoothing factor which controls its behaviour, and the aim of our Note is to construct some data-driven criterion for choosing this smoothing parameter. The criterion can be formulated in terms of a functional version of cross-validation ideas. Under mild assumptions on the unknown regression operator, it is seen that this rule is asymptotically optimal. As by-products of this result, we state asymptotic equivalences for several measures of accuracy for nonparametric estimate of the regression operator. To cite this article: M. Rachdi, P. Vieu, C. R. Acad. Sci. Paris, Ser. I 341 (2005).