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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.
| 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 |
| Publication 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 |
