Bootstrap-based Inference for Dependence in Multivariate Functional Data

30/2018

Bootstrap-based Inference for Dependence in Multivariate Functional Data

Saturday 12th May 2018

Ieva, F.; Palma, F.; Romo, J.

In this work, we propose a bootstrap based inferential framework for quantifying dependency among families of multivariate curves.We start from the notion of Spearman index and Spearman Matrix to provide pointwise estimates of dependency among families of (multivariate) curves, enabling the analysis of the pattern of dependence among the components of a multivariate functional dataset. Moreover, a suitable inferential framework for the Spearman index and matrix is proposed, making use of a testing procedure based on adjusted confidence intervals for the Spearman index. An additional bootstrap based test for the matrices, enabling the detection of significant differencies in the patterns of dependency among components in different families of multivariate curves is provided. We apply these procedures to a real case study, where two populations of electrocardiographic signals from healthy and unhealthy patients are compared. All the codes are embedded in a suitable R-package, namely raohd. The inferential tools presented in this work represent, to the best of our knowledge, the first systematic attempt to investigate dependency in the (multivariate) functional setting.