Open Access
June 2012 Minimax signal detection in ill-posed inverse problems
Yuri I. Ingster, Theofanis Sapatinas, Irina A. Suslina
Ann. Statist. 40(3): 1524-1549 (June 2012). DOI: 10.1214/12-AOS1011


Ill-posed inverse problems arise in various scientific fields. We consider the signal detection problem for mildly, severely and extremely ill-posed inverse problems with $l^{q}$-ellipsoids (bodies), $q\in(0,2]$, for Sobolev, analytic and generalized analytic classes of functions under the Gaussian white noise model. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived tests are, often, nonadaptive. Minimax rate-optimal adaptive tests of rather simple structure are also constructed.


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Yuri I. Ingster. Theofanis Sapatinas. Irina A. Suslina. "Minimax signal detection in ill-posed inverse problems." Ann. Statist. 40 (3) 1524 - 1549, June 2012.


Published: June 2012
First available in Project Euclid: 5 September 2012

zbMATH: 1297.62097
MathSciNet: MR3015034
Digital Object Identifier: 10.1214/12-AOS1011

Primary: 62G10 , 62G20
Secondary: 62C20

Keywords: analytic functions , Ill-posed inverse problems , minimax testing , Singular value decomposition , Sobolev Spaces

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 3 • June 2012
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