The Annals of Statistics

Nonlinear estimation for linear inverse problems with error in the operator

Marc Hoffmann and Markus Reiss

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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.

Article information

Ann. Statist., Volume 36, Number 1 (2008), 310-336.

First available in Project Euclid: 1 February 2008

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Zentralblatt MATH identifier

Primary: 65J20: Improperly posed problems; regularization 62G07: Density estimation

Statistical inverse problem Galerkin projection method wavelet thresholding minimax rate degree of ill-posedness matrix compression


Hoffmann, Marc; Reiss, Markus. Nonlinear estimation for linear inverse problems with error in the operator. Ann. Statist. 36 (2008), no. 1, 310--336. doi:10.1214/009053607000000721.

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