Canonical Correlation Analysis Through Linear Modeling

Keunbaik Lee, Jae Keun Yoo

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish
Pages (from-to)59-72
Number of pages14
JournalAustralian and New Zealand Journal of Statistics
Issue number1
StatePublished - Mar 2014


  • Canonical correlation
  • Least squares
  • Multivariate regression
  • Sufficient dimension reduction
  • Variable selection


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