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Title: A bootstrap approach to the inference on dependence in a multivariate functional setting Authors:  Francesca Ieva - Politecnico di Milano (Italy) [presenting]
Juan Romo - Universidad Carlos III de Madrid (Spain)
Francesco Palma - Politecnico di Milano (Italy)
Abstract: An inferential bootstrap-based procedure is presented for the of Spearman index, i.e., an index which aims to quantify the level of dependence between two families of functional data. We provide point and interval estimators of the index in order to check, through suitable tests, if two families of functional data can be considered as being independent. We introduce the new notion of Spearman Matrix (SM), which enables us to describe the pattern of dependence among the components of a multivariate functional dataset. A simulation study aimed at testing the performance of the Spearman index and matrix in correctly detecting the dependence is also provided. Finally, SM is used to analyze two different populations of multivariate curves (specifically, Electrocardiographic signals of healthy and unhealthy people), in order to check if the patterns of dependence between the components are different in the two cases. This is done by providing the results of suitable hypothesis tests verifying the equality between the Spearman matrices of the two populations.