Modern multivariate statistical analysis, a graduate course and handbook
Modern multivariate statistical analysis, a graduate course and handbook
Journal of Multivariate Analysis
A local parameterization of Orthogonal and semi-orthogonal matrices with applications
Journal of Multivariate Analysis
Asymptotic theory for canonical correlations analysis
Journal of Multivariate Analysis
A chi-square test for dimensionality with non-Gaussian data
Journal of Multivariate Analysis
Latent models for cross-covariance
Journal of Multivariate Analysis
On the estimators of model-based and maximal reliability
Journal of Multivariate Analysis
Accurate distribution and its asymptotic expansion for the tetrachoric correlation coefficient
Journal of Multivariate Analysis
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Asymptotic expansions of the distributions of typical estimators in canonical correlation analysis under nonnormality are obtained. The expansions include the Edgeworth expansions up to order O(1/n) for the parameter estimators standardized by the population standard errors, and the corresponding expansion by Hall's method with variable transformation. The expansions for the Studentized estimators are also given using the Cornish-Fisher expansion and Hall's method. The parameter estimators are dealt with in the context of estimation for the covariance structure in canonical correlation analysis. The distributions of the associated statistics (the structure of the canonical variables, the scaled log likelihood ratio and Rozeboom's between-set correlation) are also expanded. The robustness of the normal-theory asymptotic variances of the sample canonical correlations and associated statistics are shown when a latent variable model holds. Simulations are performed to see the accuracy of the asymptotic results in finite samples.