B1914
Title: A Spearman dependence matrix for multivariate functional data
Authors: Francesca Ieva - Politecnico di Milano (Italy)
Juan Romo - Universidad Carlos III de Madrid (Spain)
Anna Maria Paganoni - MOX-Politecnico di Milano (Italy) [presenting]
Abstract: An innovative nonparametric inferential framework is presented, designed to quantify dependence within two distinct families of multivariate functional data. The framework extends the conventional Spearman correlation coefficient concept to scenarios where the observations are curves generated by stochastic processes. In particular, several properties of the Spearman index are illustrated emphasizing the importance of having a consistent estimator of the index of the original processes. The notion of the Spearman index is used to define the Spearman matrix, a mathematical entity expressing the pattern of dependence among the components of a multivariate functional dataset. A simulation study is also presented to (a) rigorously assess the performance of the Spearman index across various scenarios in accurately detecting the underlying patterns of dependence within bivariate functional datasets and (b) to assess the robustness of the Spearman coefficient when confronted with different types of outliers. Lastly, the concept of the Spearman matrix is leveraged to conduct an in-depth analysis of two distinct 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.
