Applied multivariate statistical analysis
Applied multivariate statistical analysis
Journal of Multivariate Analysis
Asymptotic theory for canonical correlations analysis
Journal of Multivariate Analysis
Influence function and efficiency of the minimum covariance determinant scatter matrix estimator
Journal of Multivariate Analysis
The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies
Journal of Multivariate Analysis
Robust estimation of Cronbach's alpha
Journal of Multivariate Analysis
Robust dimension reduction based on canonical correlation
Journal of Multivariate Analysis
Optimal tests for homogeneity of covariance, scale, and shape
Journal of Multivariate Analysis
Asymptotic distributions of robust shape matrices and scales
Journal of Multivariate Analysis
Asymptotic expansion of the minimum covariance determinant estimators
Journal of Multivariate Analysis
Asymptotic properties of canonical correlation analysis for one group with additional observations
Journal of Multivariate Analysis
Ensemble canonical correlation analysis
Applied Intelligence
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In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example.