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Canonical Correlation Analysis Through Linear Modeling
Author(s) -
Lee Keunbaik,
Yoo Jae Keun
Publication year - 2014
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12057
Subject(s) - mathematics , canonical correlation , canonical analysis , canonical form , estimator , test statistic , canonical correspondence analysis , linear model , statistics , general linear model , statistical hypothesis testing , pure mathematics , fishery , abundance (ecology) , biology
Summary In this paper, we introduce linear modeling of canonical correlation analysis, which estimates canonical direction matrices by minimising a quadratic objective function. The linear modeling results in a class of estimators of canonical direction matrices, and an optimal class is derived in the sense described herein. The optimal class guarantees several of the following desirable advantages: first, its estimates of canonical direction matrices are asymptotically efficient; second, its test statistic for determining the number of canonical covariates always has a chi‐squared distribution asymptotically; third, it is straight forward to construct tests for variable selection. The standard canonical correlation analysis and other existing methods turn out to be suboptimal members of the class. Finally, we study the role of canonical variates as a means of dimension reduction for predictors and responses in multivariate regression. Numerical studies and data analysis are presented.