Electronic Journal of Statistics

On signal detection and confidence sets for low rank inference problems

Alexandra Carpentier and Richard Nickl

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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.

Article information

Electron. J. Statist., Volume 9, Number 2 (2015), 2675-2688.

Received: July 2015
First available in Project Euclid: 8 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G15: Tolerance and confidence regions
Secondary: 62G10: Hypothesis testing

Low rank matrices confidence sets signal detection nuclear norm


Carpentier, Alexandra; Nickl, Richard. On signal detection and confidence sets for low rank inference problems. Electron. J. Statist. 9 (2015), no. 2, 2675--2688. doi:10.1214/15-EJS1087. https://projecteuclid.org/euclid.ejs/1449582159

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