Sparse Reduced-Rank Regression for Simultaneous Dimension Reduction and Variable Selection Academic Article uri icon

abstract

  • The reduced-rank regression is an effective method in predicting multiple response variables from the same set of predictor variables. It reduces the number of model parameters and takes advantage of interrelations between the response variables and hence improves predictive accuracy. We propose to select relevant variables for reduced-rank regression by using a sparsity-inducing penalty. We apply a group-lasso type penalty that treats each row of the matrix of the regression coefficients as a group and show that this penalty satisfies certain desirable invariance properties. We develop two numerical algorithms to solve the penalized regression problem and establish the asymptotic consistency of the proposed method. In particular, the manifold structure of the reduced-rank regression coefficient matrix is considered and studied in our theoretical analysis. In our simulation study and real data analysis, the new method is compared with several existing variable selection methods for multivariate regression and exhibits competitive performance in prediction and variable selection. © 2012 American Statistical Association.

altmetric score

  • 0.5

author list (cited authors)

  • Chen, L., & Huang, J. Z.

citation count

  • 111

complete list of authors

  • Chen, Lisha||Huang, Jianhua Z

publication date

  • October 2012