High dimensional density estimation and curve classification.

Summary The objective of this thesis is to study and extend density estimation and classification techniques in high dimensional spaces. We have chosen to structure our work in three parts. The first part, entitled complements on modified histograms, is composed of two chapters devoted to the study of a family of nonparametric density estimators, the modified histograms, which are known to have good convergence properties in the sense of the information theory criteria. In the first chapter, these estimators are considered as dynamic systems of infinite dimensional state space. The second chapter is devoted to the study of these estimators for dimensions greater than one. The second part of the thesis, entitled combinatorial methods in density estimation, is divided into two chapters. We are interested in the finite distance performance of density estimators selected from a family of candidate estimators, whose cardinal is not necessarily finite. In the first chapter, we study the performance of these methods in the context of the selection of different parameters of modified histograms. In the second chapter, we continue with the selection of kernel estimators whose smoothing parameter adapts locally to the estimation point and to the data. Finally, the third and last part, more applied and independent of the previous ones, presents a new method allowing to classify curves from a decomposition of the observations in wavelet bases.