Multivariate Regression Shrinkage and Selection by Canonical Correlation Analysis

31 Pages Posted: 23 Dec 2012

See all articles by Baiguo An

Baiguo An

Capital University of Economics and Business

Guo Jianhua

Northeast Normal University

Hansheng Wang

Peking University - Guanghua School of Management

Date Written: December 23, 2012

Abstract

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.

Keywords: Adaptive Lasso, Canonical Correlation Analysis, Multivariate Regression, Selection Consistency, Tuning Parameter Selection

JEL Classification: C10, C13

Suggested Citation

An, Baiguo and Jianhua, Guo and Wang, Hansheng, Multivariate Regression Shrinkage and Selection by Canonical Correlation Analysis (December 23, 2012). Available at SSRN: https://ssrn.com/abstract=2193372 or http://dx.doi.org/10.2139/ssrn.2193372

Baiguo An

Capital University of Economics and Business ( email )

Capital University of Economics and Business
Beijing, Beijing
China

Guo Jianhua

Northeast Normal University ( email )

Changchun
China

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

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