Aggregating estimates by convex optimization
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Publication:6372980
DOI10.4171/MSL/30arXiv2107.07836MaRDI QIDQ6372980
Anatoli Juditsky, Arkadi Nemirovski
Publication date: 16 July 2021
Abstract: We discuss the approach to estimate aggregation and adaptive estimation based upon (nearly optimal) testing of convex hypotheses. We show that in the situation where the observations stem from {em simple observation schemes} and where set of unknown signals is a finite union of convex and compact sets, the proposed approach leads to aggregation and adaptation routines with nearly optimal performance. As an illustration, we consider application of the proposed estimates to the problem of recovery of unknown signal known to belong to a union of ellitopes in Gaussian observation scheme. The proposed approach can be implemented efficiently when the number of sets in the union is "not very large." We conclude the paper with a small simulation study illustrating practical performance of the proposed procedures in the problem of signal estimation in the single-index model.
Nonparametric hypothesis testing (62G10) Nonparametric estimation (62G05) Applications of mathematical programming (90C90)
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