Sparse Multivariate Regression With Covariance Estimation

作者：Rothman Adam J^*; Levina Elizaveta; Zhu Ji

来源：Journal of Computational and Graphical Statistics, 2010, 19(4): 947-962.

DOI：10.1198/jcgs.2010.09188

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

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.

• 出版日期2010-12