Abstract
Functional canonical correlation analysis (FCCA) is a tool for exploring the associations between a pair of functional data. However, when the association is nonlinear or even nonmonotone, FCCA can fail to discover any meaningful relationship between the pair. In this paper, nonlinear FCCA estimators are constructed based on some popular measures of dependence — distance covariance and distance correlation. Consistency of the estimators is shown. Numerical studies are presented that demonstrate nonlinear FCCA can uncover new association patterns between functional covariates.
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