Volume 14, 2010
|Page(s)||173 - 191|
|Published online||29 July 2010|
Penalized estimators for non linear inverse problems
Institut de Mathématiques, Équipe de Statistique et Probabilités, Université Paul Sabatier, 31000 Toulouse, France
2 Departamento de Matemáticas, IVIC, Venezuela
Revised: 9 October 2007
Revised: 16 March 2008
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.
Mathematics Subject Classification: 60G17 / 62G07
Key words: Ill-posed Inverse Problems / Tikhonov estimator / projection estimator / penalized estimation / model selection
© EDP Sciences, SMAI, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.