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On signal detection and confidence sets for low rank inference problems
- We consider the signal detection problem in the Gaussian design trace regression model with low rank alternative hypotheses. We derive the precise (Ingster-type) detection boundary for the Frobenius and the nuclear norm. We then apply these results to show that honest confidence sets for the unknown matrix parameter that adapt to all low rank sub-models in nuclear norm do not exist. This shows that recently obtained positive results in [5] for confidence sets in low rank recovery problems are essentially optimal.
| Author details: | Alexandra CarpentierORCiDGND, Richard Nickl |
|---|---|
| DOI: | https://doi.org/10.1214/15-EJS1087 |
| ISSN: | 1935-7524 |
| Title of parent work (English): | Electronic journal of statistics |
| Publisher: | Institute of Mathematical Statistics |
| Place of publishing: | Cleveland |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2015 |
| Publication year: | 2015 |
| Release date: | 2017/03/27 |
| Tag: | Low rank matrices; confidence sets; nuclear norm; signal detection |
| Volume: | 9 |
| Issue: | 2 |
| Number of pages: | 14 |
| First page: | 2675 |
| Last Page: | 2688 |
| Funding institution: | European Research Council (ERC) [647812]; DFG (Deutsche Forschungsgemeinschaft) |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access |
