Sparse multivariate regression with covariance estimation

Adam J. Rothman, Elizaveta Levina, Ji Zhu

Research output: Contribution to journalArticlepeer-review

233 Scopus citations


We propose a procedure for constructing a sparse estimator of a multivariate regression coefficient matrix that accounts for correlation of the response variables. This method, which we call multivariate regression with covariance estimation (MRCE), involves penalized likelihood with simultaneous estimation of the regression coefficients and the covariance structure. An efficient optimization algorithm and a fast approximation are developed for computing MRCE. Using simulation studies, we show that the proposed method outperforms relevant competitors when the responses are highly correlated. We also apply the new method to a finance example on predicting asset returns. An R-package containing this dataset and code for computing MRCE and its approximation are available online.

Original languageEnglish (US)
Pages (from-to)947-962
Number of pages16
JournalJournal of Computational and Graphical Statistics
Issue number4
StatePublished - Dec 2010

Bibliographical note

Funding Information:
We thank Ming Yuan for providing the weekly log-returns dataset. We also thank the associate editor and two referees for their helpful suggestions. This research has been supported in part by the Yahoo Ph.D. student fellowship (A. J. Rothman) and National Science Foundation grants DMS-0805798 (E. Levina), DMS-0705532 and DMS-0748389 (J. Zhu).


  • High dimension low sample size
  • Lasso
  • Multiple output regression
  • Sparsity


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