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August 2006 Risk hull method and regularization by projections of ill-posed inverse problems
L. Cavalier, Yu. Golubev
Ann. Statist. 34(4): 1653-1677 (August 2006). DOI: 10.1214/009053606000000542


We study a standard method of regularization by projections of the linear inverse problem Y=Af+ε, where ε is a white Gaussian noise, and A is a known compact operator with singular values converging to zero with polynomial decay. The unknown function f is recovered by a projection method using the singular value decomposition of A. The bandwidth choice of this projection regularization is governed by a data-driven procedure which is based on the principle of risk hull minimization. We provide nonasymptotic upper bounds for the mean square risk of this method and we show, in particular, that in numerical simulations this approach may substantially improve the classical method of unbiased risk estimation.


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L. Cavalier. Yu. Golubev. "Risk hull method and regularization by projections of ill-posed inverse problems." Ann. Statist. 34 (4) 1653 - 1677, August 2006.


Published: August 2006
First available in Project Euclid: 3 November 2006

zbMATH: 1246.62082
MathSciNet: MR2283712
Digital Object Identifier: 10.1214/009053606000000542

Primary: 62G05 , 62G20

Keywords: inverse problem , Oracle inequality , quadratic risk , risk hull

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 4 • August 2006
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