Canonical Correlation Analysis when the Data are Curves

It is not immediately straightforward to extend canonical correlation analysis to the context of functional data analysis, where the data are themselves curves or functions. The obvious approach breaks down, and it is necessary to use a method involving smoothing in some way. Such a method is introduced and discussed with reference to a data set on human gait. The breakdown of the unsmoothed method is illustrated in a practical context and is demonstrated theoretically. A consistency theorem for the smoothed method is proved.