Electronic Journal of Statistics

Low rank multivariate regression

Christophe Giraud

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Abstract

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.

Article information

Source
Electron. J. Statist., Volume 5 (2011), 775-799.

Dates
First available in Project Euclid: 8 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1312818918

Digital Object Identifier
doi:10.1214/11-EJS625

Mathematical Reviews number (MathSciNet)
MR2824816

Zentralblatt MATH identifier
1274.62434

Subjects
Primary: 62H99: None of the above, but in this section 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 62J05: Linear regression

Keywords
Multivariate regression random matrix Ky-Fan norms estimator selection

Citation

Giraud, Christophe. Low rank multivariate regression. Electron. J. Statist. 5 (2011), 775--799. doi:10.1214/11-EJS625. https://projecteuclid.org/euclid.ejs/1312818918


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