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Two methods are given for the estimation of the dimensionality in canonical correlation analysis. One is based on Mallows's Cp statistic in regression. The other uses an information criterion for choice of models. Monte Carlo comparison of the sequential Bartlett-Lawley test procedure and the two methods are presented. The two methods are applied to the estimation of the dimensionality in canonical variate analysis.
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Fujikoshi et al. (1979) studied this question.
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