On local influence in canonical correlation analysis

Influence analysis based on Cook's local influence is developed by using the. likelihood displacement as the criterion function for studying jointly as well as singly influential observations in canonical correlation analysis (CCA) assuming two types of case-weight perturbation. It is found that the results of the influence analysis are invariant under affine transformations of variables just as the results of CCA itself and that the derived influential directions are equivalent to the vectors of principal component scores of the influence functions of CCA parameters (phi) under bar obtained by principal component analysis with metric V-, where V is the asymptotic variance-covariance matrix of (phi) under bar and the superscript(-) indicates a generalized inverse. A numerical example is shown to illustrate the proposed method.