## The Annals of Statistics

### Minimax signal detection in ill-posed inverse problems

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 5 September 2012

https://projecteuclid.org/euclid.aos/1346850064

Digital Object Identifier
doi:10.1214/12-AOS1011

Mathematical Reviews number (MathSciNet)
MR3015034

Zentralblatt MATH identifier
1297.62097

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

#### Citation

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. https://projecteuclid.org/euclid.aos/1346850064

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