Adaptive confidence sets for matrix completion

  • In the present paper, we study the problem of existence of honest and adaptive confidence sets for matrix completion. We consider two statistical models: the trace regression model and the Bernoulli model. In the trace regression model, we show that honest confidence sets that adapt to the unknown rank of the matrix exist even when the error variance is unknown. Contrary to this, we prove that in the Bernoulli model, honest and adaptive confidence sets exist only when the error variance is known a priori. In the course of our proofs, we obtain bounds for the minimax rates of certain composite hypothesis testing problems arising in low rank inference.

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Metadaten
Author details:Alexandra CarpentierORCiDGND, Olga KloppGND, Matthias LöfflerGND, Richard NicklGND
DOI:https://doi.org/10.3150/17-BEJ933
ISSN:1350-7265
ISSN:1573-9759
Title of parent work (English):Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
Publisher:International Statistical Institute
Place of publishing:Voorburg
Publication type:Article
Language:English
Date of first publication:2018/03/26
Completion year:2018
Release date:2021/07/20
Tag:adaptivity; confidence sets; low rank recovery; matrix completion; minimax hypothesis testing; unknown variance
Volume:24
Issue:4A
Number of pages:32
First page:2429
Last Page:2460
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Peer review:Referiert
Publishing method:Open Access / Green Open-Access