Low rank Multivariate regression

Details Low rank Multivariate regression Low rank Multivariate regression

2010-09-27

arxiv.org/abs/1009.5165v2

Mathematics

Statistics Theory

23 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Low rank Multivariate regression does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Low rank Multivariate regression, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Low rank Multivariate regression will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-517617