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.

中文翻译：

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基于距离协方差的非线性函数典型相关分析

功能典型相关分析 (FCCA) 是一种用于探索一对功能数据之间关联的工具。然而，当关联是非线性的甚至是非单调的时，FCCA 可能无法发现这对之间的任何有意义的关系。在本文中，非线性 FCCA 估计器是基于一些流行的依赖度量——距离协方差和距离相关性构建的。显示了估计量的一致性。数值研究表明非线性 FCCA 可以揭示功能协变量之间的新关联模式。