Sparse Reduced-Rank Regression for Simultaneous Dimension Reduction and Variable Selection

• 成果类型: Article
• 署名作者: Chen, Lisha; Huang, Jianhua Z.
• 署名单位: Yale University; Texas A&M University System; Texas A&M University College Station
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.734178
• 发表日期: 2012
• 页码: 1533-1545
• 关键词: multivariate regression; shrinkage

摘要

The reduced-rank regression is an effective method in predicting multiple response variables from the same set of predictor variables. It reduces the dumber 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.