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February 2008 Nonlinear estimation for linear inverse problems with error in the operator
Marc Hoffmann, Markus Reiss
Ann. Statist. 36(1): 310-336 (February 2008). DOI: 10.1214/009053607000000721


We study two nonlinear methods for statistical linear inverse problems when the operator is not known. The two constructions combine Galerkin regularization and wavelet thresholding. Their performances depend on the underlying structure of the operator, quantified by an index of sparsity. We prove their rate-optimality and adaptivity properties over Besov classes.


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Marc Hoffmann. Markus Reiss. "Nonlinear estimation for linear inverse problems with error in the operator." Ann. Statist. 36 (1) 310 - 336, February 2008.


Published: February 2008
First available in Project Euclid: 1 February 2008

zbMATH: 1134.65038
MathSciNet: MR2387973
Digital Object Identifier: 10.1214/009053607000000721

Primary: 62G07 , 65J20

Keywords: degree of ill-posedness , Galerkin projection method , matrix compression , Minimax rate , Statistical inverse problem , wavelet thresholding

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 1 • February 2008
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