2010/09/27 by Christophe Giraud, Giraud, Christophe
Engineering · Mathematics · #FOS: Mathematics #Mathematical Inequalities and Applications #Random Matrices and Applications #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1009.5165
openalex publication_date 2010/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 the Ky-Fan quasi-norm 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.