Multivariate regression shrinkage and selection by canonical correlation analysis

作者：An, Baiguo; Guo, Jianhua^*; Wang, Hansheng

来源：Computational Statistics & Data Analysis, 2013, 62: 93-107.

DOI：10.1016/j.csda.2012.12.017

• Adaptive lasso
• Canonical correlation analysis
• Multivariate regression
• Selection consistency
• Tuning parameter selection

The problem of regression shrinkage and selection for multivariate regression is considered. The goal is to consistently identify those variables relevant for regression. This is done not only for predictors but also for responses. To this end, a novel relationship between multivariate regression and canonical correlation is discovered. Subsequently, its equivalent least squares type formulation is constructed, and then the well developed adaptive LASSO type penalty and also a novel BIC-type selection criterion can be directly applied. Theoretical results show that the resulting estimator is selection consistent for not only predictors but also responses. Numerical studies are presented to corroborate our theoretical findings.

• 出版日期2013-6
• 单位北京大学; 东北师范大学