MINIMAX SIGNAL DETECTION IN ILL-POSED INVERSE PROBLEMS

• 成果类型: Article
• 署名作者: Ingster, Yuri I.; Sapatinas, Theofanis; Suslina, Irina A.
• 署名单位: Saint Petersburg State Electrotechnical University; University of Cyprus; ITMO University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1011
• 发表日期: 2012
• 页码: 1524-1549
• 关键词: NOISE

摘要

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 is an element of (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.