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Estimation non paramétrique et problèmes inverses

Abstract : Nonparametric estimation problems
for inverse models consist in recovering an unknown function from
the observation of a linear ill posed transformation of the
function, blurred by an additive random error. In this context,
wavelet methods are very useful and have been widely studied. The
estimators developed in this thesis are significantly influenced
by them, but also stray from decompositions in "classical" wavelet
bases, which allows new theoretical and practical developments. In
a main part of the thesis, one focuses on a white noise type
model. One develops estimators using bases which, on the one hand
are adapted to the operator of the problem, and on the other hand
possess wavelet type properties. One investigates the theoretical
properties of such methods in a wide minimax framework, as well as
their numerical performances, by a simulation study. In the last
part of the thesis, one focuses on the model of regression in
random design, and one investigates the numerical performances of
an estimator based on the "warping" of wavelet bases.
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Contributor : Thomas Willer <>
Submitted on : Tuesday, December 19, 2006 - 5:06:16 PM
Last modification on : Wednesday, December 9, 2020 - 3:14:34 PM
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  • HAL Id : tel-00121197, version 1


Thomas Willer. Estimation non paramétrique et problèmes inverses. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2006. Français. ⟨tel-00121197⟩



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