Penalized estimators for non linear inverse problems

Jean-Michel Loubes; Carenne Ludeña

ESAIM: Probability and Statistics (2010)

  • Volume: 14, page 173-191
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Loubes, Jean-Michel, and Ludeña, Carenne. "Penalized estimators for non linear inverse problems." ESAIM: Probability and Statistics 14 (2010): 173-191. <http://eudml.org/doc/250857>.

@article{Loubes2010,
abstract = { 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. },
author = {Loubes, Jean-Michel, Ludeña, Carenne},
journal = {ESAIM: Probability and Statistics},
keywords = {Ill-posed Inverse Problems; Tikhonov estimator; projection estimator; penalized estimation; model selection; ill-posed inverse problems; projection estimator},
language = {eng},
month = {7},
pages = {173-191},
publisher = {EDP Sciences},
title = {Penalized estimators for non linear inverse problems},
url = {http://eudml.org/doc/250857},
volume = {14},
year = {2010},
}

TY - JOUR
AU - Loubes, Jean-Michel
AU - Ludeña, Carenne
TI - Penalized estimators for non linear inverse problems
JO - ESAIM: Probability and Statistics
DA - 2010/7//
PB - EDP Sciences
VL - 14
SP - 173
EP - 191
AB - 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.
LA - eng
KW - Ill-posed Inverse Problems; Tikhonov estimator; projection estimator; penalized estimation; model selection; ill-posed inverse problems; projection estimator
UR - http://eudml.org/doc/250857
ER -

References

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