Open Access
2011 Low rank multivariate regression
Christophe Giraud
Electron. J. Statist. 5: 775-799 (2011). DOI: 10.1214/11-EJS625


We consider in this paper the multivariate regression problem, when the target regression matrix A is close to a low rank matrix. Our primary interest is in on the practical case where the variance of the noise is unknown. Our main contribution is to propose in this setting a criterion to select among a family of low rank estimators and prove a non-asymptotic oracle inequality for the resulting estimator. We also investigate the easier case where the variance of the noise is known and outline that the penalties appearing in our criterions are minimal (in some sense). These penalties involve the expected value of Ky-Fan norms of some random matrices. These quantities can be evaluated easily in practice and upper-bounds can be derived from recent results in random matrix theory.


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Christophe Giraud. "Low rank multivariate regression." Electron. J. Statist. 5 775 - 799, 2011.


Published: 2011
First available in Project Euclid: 8 August 2011

zbMATH: 1274.62434
MathSciNet: MR2824816
Digital Object Identifier: 10.1214/11-EJS625

Primary: 60B20 , 62H99 , 62J05

Keywords: Estimator selection , Ky-Fan norms , multivariate regression , Random matrix

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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