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# Quelques aspects fonctionnels et non fonctionnels des grandes déviations et des déviations modérées en estimation non-paramétrique

Abstract : This thesis deals with functional and nonfunctional spects of large and moderate deviation in nonparametric function estimation. We introduce a process which allows to derive in an unified way pointwise and functional large deviation principles and pointwise and uniform Chernoff type results for the density and regression function estimates. In first step, we establish a functional large deviations principle for the kernel estimate of the regression function indexed by a family of functions satisfying Arzèla-Ascoli conditions. Subsequently, the results have been applied to define a large deviations selection model criterion. In the second part, we investigate large deviation behaviours related to the density and regression function estimates using the histogram method. Here, large deviation principles, ponitwise and uniform chernoff type results as well as minimax bounds for both estimates have been stated. In the two last chapters, functional large deviation principles in the $L^1$-space endowed with the weak topology for the delta sequences density and regression function estimates as well as a functional moderate deviations principle for the histogram density estimate have been stated.
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https://tel.archives-ouvertes.fr/tel-00266890
Contributor : Sidi Mohamed Ould Maouloud <>
Submitted on : Tuesday, March 25, 2008 - 5:34:26 PM
Last modification on : Monday, December 14, 2020 - 9:52:35 AM
Long-term archiving on: : Thursday, May 20, 2010 - 10:28:47 PM

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• HAL Id : tel-00266890, version 1

### Citation

Sidi Mohamed Ould Maouloud. Quelques aspects fonctionnels et non fonctionnels des grandes déviations et des déviations modérées en estimation non-paramétrique. Mathématiques [math]. Université de Reims - Champagne Ardenne, 2007. Français. ⟨tel-00266890⟩

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