Journal
COMPUTATIONAL STATISTICS & DATA ANALYSIS
Volume 62, Issue -, Pages 93-107Publisher
ELSEVIER
DOI: 10.1016/j.csda.2012.12.017
Keywords
Adaptive lasso; Canonical correlation analysis; Multivariate regression; Selection consistency; Tuning parameter selection
Funding
- National Natural Science Foundation of China [11025102, 11226216, 11131002, 11271032]
- PCSIRT
- Jilin Project [20100401]
- Fox Ying Tong Education Foundation
- Fundamental Research Funds for the Central Universities
- Research Funds of Renmin University of China
- Center for Statistical Science at Peking University
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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. (C) 2013 Elsevier B.V. All rights reserved.
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