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Estimation de densité en dimension élevée et classification de courbes

Abstract : The goal of this thesis is to study and develop methods for density estimation and curve classification in higher dimensions. This study is structured into three parts.

The first part, entitled complements on modified histograms, is organized in two chapters and is devoted to the study of a family of nonparametric density estimates, namely modified histograms. These estimates are known to have good consistency properties according to information theoretic criteria. In the first chapter, these estimates are viewed as dynamical systems with infinite dimensional state space. The second chapter deals with the study of these estimates for dimensions greater than one.

The second part of this thesis, entitled combinatorial methods in density estimation, is divided into two chapters. We are interested in nonasymptotic error bounds for density estimates selected within a family of candidates (not necessary finite). In the first chapter, we study the performance of these methods in selecting the free parameters of the modified histograms. We continue, in the second chapter, with the selection of kernel density estimates using bandwidths which vary with the location and the data.

The third and last part, more applied and independent of the preceding ones, provides a new method which allows us to classify curves by expanding the sample data on a wavelet basis.
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Contributor : Laurent Rouvière <>
Submitted on : Wednesday, February 15, 2006 - 6:38:27 PM
Last modification on : Thursday, January 11, 2018 - 6:15:40 AM
Long-term archiving on: : Saturday, April 3, 2010 - 10:25:03 PM


  • HAL Id : tel-00011624, version 1


Laurent Rouviere. Estimation de densité en dimension élevée et classification de courbes. Mathématiques [math]. Université Montpellier II - Sciences et Techniques du Languedoc, 2005. Français. ⟨tel-00011624⟩



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