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Contribution à l'étude de la régression non paramétrique et à l'estimation de la moyenne d'un processus à temps continu

Abstract : The present PhD deals with nonparametric regression using repeated measurements data. On the one hand, the convergence rates of several usual estimators found in the litterature under classical dependency assumptions are extended to the smoothing spline estimators. On the other hand, in the context of mean function estimation from continuous-time random processes, the few existing results on mean square convergence are generalized to a large class of linear estimators and new asymptotic normality results are derived for the finite-dimensional distributions of estimators. Finally in the framework of a finite, correlated sample, the ordinary and generalized least squares methods for constructing regression estimators are compared, a new smoothing parameter selection procedure accounting for the covariance structure of the data is presented, and the superiority of local smoothing over global smoothing is shown through simulations.
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https://tel.archives-ouvertes.fr/tel-00201438
Contributor : David Degras <>
Submitted on : Friday, December 28, 2007 - 6:24:31 PM
Last modification on : Wednesday, December 9, 2020 - 3:06:00 PM
Long-term archiving on: : Thursday, September 27, 2012 - 1:30:10 PM

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  • HAL Id : tel-00201438, version 1

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David Degras. Contribution à l'étude de la régression non paramétrique et à l'estimation de la moyenne d'un processus à temps continu. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2007. Français. ⟨tel-00201438⟩

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