Methods of canonical analysis for functional data

We consider estimates for functional canonical correlations and canonical weight functions. Four computational methods for the estimation of functional canonical correlation and canonical weight functions are proposed and compared, including one which is a slight variation of the spline method proposed by Leurgans et al. (J. Roy. Statist. Soc. Ser. B 55 (1993) 725). We propose dimension reduction and dimension augmentation procedures to address the dimensionality problems of functional canonical analysis (FCA) that are associated with computational break-down. Cross-validation is used for the automatic selection of tuning parameters, based on the minimax property of FCA. This allows to estimate several canonical correlations and canonical weight functions simultaneously and reasonably well as we show in simulations. The proposed estimation methods are compared and their use is demonstrated with medfly mortality data. (C) 2003 Elsevier B.V. All rights reserved.