Reduction of Dimensionality under Multivariate Regression and Canonical Correlation Models

摘要

In this paper, the author gives a review of the literature on various techniques for determination of the ranks of regression matrix and canonical correlation matrix. Also, methods of selection of important original variables under multivariate regression and canonical correlation models are reviewed. The methods reviewed involve not only tests of hypotheses but also model selection methods based upon information theoretic criteria. Keywords: Contingency tables; correlated multivariate regression equations model; discriminant analysis; econometrics; likelihood ratio test; linear and structural relations; pattern recognition; random effects model. (Author)