A Spearman dependence matrix for multivariate functional data

We propose a nonparametric inferential framework for quantifying dependence among two families of multivariate functional data. We generalize the notion of Spearman correlation coefficient to situations where the observations are curves generated by a stochastic processes. In particular, several properties of the Spearman index are illustrated emphasizing the importance of having a consistent estimator of the index. We use the notion of Spearman index to define the Spearman matrix, a mathematical object expressing the pattern of dependence among the components of a multivariate functional dataset. Finally, the notion of Spearman matrix is exploited to analyze two different populations of multivariate curves (specifically, Electrocardiographic signals of healthy and unhealthy people), in order to test if the pattern of dependence between the components is statistically different in the two cases.