# 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

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topLoubes, 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 -

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