Electronic Journal of Statistics

Adaptive complexity regularization for linear inverse problems

Jean-Michel Loubes and Carenne Ludeña

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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

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

First available in Project Euclid: 30 July 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 34K29: Inverse problems

Inverse Problems Adaptive Estimation Regularization


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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