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Media type:
E-Article
Title:
MINIMAX SIGNAL DETECTION IN ILL-POSED INVERSE PROBLEMS
Contributor:
Ingster, Yuri I.;
Sapatinas, Theofanis;
Suslina, Irina A.
Published:
Institute of Mathematical Statistics, 2012
Published in:
The Annals of Statistics, 40 (2012) 3, Seite 1524-1549
Language:
English
ISSN:
0090-5364
Origination:
Footnote:
Description:
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 є (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.