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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. 相似文献