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2015 On signal detection and confidence sets for low rank inference problems
Alexandra Carpentier, Richard Nickl
Electron. J. Statist. 9(2): 2675-2688 (2015). DOI: 10.1214/15-EJS1087


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.


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Alexandra Carpentier. Richard Nickl. "On signal detection and confidence sets for low rank inference problems." Electron. J. Statist. 9 (2) 2675 - 2688, 2015.


Received: 1 July 2015; Published: 2015
First available in Project Euclid: 8 December 2015

zbMATH: 1329.62216
MathSciNet: MR3432430
Digital Object Identifier: 10.1214/15-EJS1087

Primary: 62G15
Secondary: 62G10

Keywords: Confidence sets , low rank matrices , nuclear norm , signal detection

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.9 • No. 2 • 2015
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