A Spearman Dependence Matrix for Multivariate Functional Data
Keywords
Statistical learning
Health Analytics
Code:
49/2023
Title:
A Spearman Dependence Matrix for Multivariate Functional Data
Date:
Wednesday 24th May 2023
Author(s):
Ieva, F.; Ronzulli, M.; Romo, J.; Paganoni, A.M.
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Abstract:
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 of the original processes. 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.