The Annals of Statistics

Minimax signal detection in ill-posed inverse problems

Yuri I. Ingster, Theofanis Sapatinas, and Irina A. Suslina

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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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Ann. Statist., Volume 40, Number 3 (2012), 1524-1549.

First available in Project Euclid: 5 September 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing 62G20: Asymptotic properties
Secondary: 62C20: Minimax procedures

Analytic functions ill-posed inverse problems minimax testing singular value decomposition Sobolev spaces


Ingster, Yuri I.; Sapatinas, Theofanis; Suslina, Irina A. Minimax signal detection in ill-posed inverse problems. Ann. Statist. 40 (2012), no. 3, 1524--1549. doi:10.1214/12-AOS1011.

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