Electronic Journal of Statistics

Adaptive complexity regularization for linear inverse problems

Jean-Michel Loubes and Carenne Ludeña

Full-text: Open access

Abstract

We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that selects the optimal smoothing sequence without prior knowledge of the regularity of the function to be estimated. We provide for such estimators oracle inequalities and optimal rates of convergence. This penalized approach is applied to Tikhonov regularization and to regularization by projection.

Article information

Source
Electron. J. Statist., Volume 2 (2008), 661-677.

Dates
First available in Project Euclid: 30 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1217450799

Digital Object Identifier
doi:10.1214/07-EJS115

Mathematical Reviews number (MathSciNet)
MR2426106

Zentralblatt MATH identifier
1320.62075

Subjects
Primary: 62G05: Estimation 34K29: Inverse problems

Keywords
Inverse Problems Adaptive Estimation Regularization

Citation

Loubes, Jean-Michel; Ludeña, Carenne. Adaptive complexity regularization for linear inverse problems. Electron. J. Statist. 2 (2008), 661--677. doi:10.1214/07-EJS115. https://projecteuclid.org/euclid.ejs/1217450799


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