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In this article we tackle the problem of inverse non linear ill-posed problems from a statistical point of view. We discuss the problem of estimating an indirectly observed function, without prior knowledge of its regularity, based on noisy observations. For this we consider two approaches: one based on the Tikhonov regularization procedure, and another one based on model selection methods for both ordered and non ordered subsets. In each case we prove consistency of the estimators and show that their rate of convergence is optimal for the given estimation procedure.
@article{PS_2010__14__173_0,
author = {Loubes, Jean-Michel and Lude\~na, Carenne},
title = {Penalized estimators for non linear inverse problems},
journal = {ESAIM: Probability and Statistics},
pages = {173--191},
publisher = {EDP-Sciences},
volume = {14},
year = {2010},
doi = {10.1051/ps:2008024},
mrnumber = {2741964},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2008024/}
}
TY - JOUR AU - Loubes, Jean-Michel AU - Ludeña, Carenne TI - Penalized estimators for non linear inverse problems JO - ESAIM: Probability and Statistics PY - 2010 SP - 173 EP - 191 VL - 14 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps:2008024/ DO - 10.1051/ps:2008024 LA - en ID - PS_2010__14__173_0 ER -
%0 Journal Article %A Loubes, Jean-Michel %A Ludeña, Carenne %T Penalized estimators for non linear inverse problems %J ESAIM: Probability and Statistics %D 2010 %P 173-191 %V 14 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps:2008024/ %R 10.1051/ps:2008024 %G en %F PS_2010__14__173_0
Loubes, Jean-Michel; Ludeña, Carenne. Penalized estimators for non linear inverse problems. ESAIM: Probability and Statistics, Tome 14 (2010), pp. 173-191. doi: 10.1051/ps:2008024
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