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some results on cononical correlations and measures of multivariate association
Authors:Song-Gui Wang  Shein-Chung Chow
Institution:1. China University of Science and Techmology ,;2. The University of Toledo ,
Abstract:The canonical correlations and several orher measures of multivariate association between two sets of variables (x and y) are considered when the covariance matrices are singular. A useful inequality for the canonical correlations when new vari- ables are brought into x or y is obtained for both the nonsingular and singular cases. It is also shown that, under a simple condition, measures of multivariate association equal one if and only if there exists a linear relationship between the sets of variables.
Keywords:singular matrix  negative definite  g-inverse  canonical correlation  measure of multivariate association (MMA)
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