Extremal correlation coefficient for functional data
Statistics Theory
2025-10-02 v3 Methodology
Statistics Theory
Abstract
We propose a coefficient that measures dependence in paired samples of functions. It has properties similar to the Pearson correlation, but differs in significant ways: (i) it is designed to measure dependence between curves, (ii) it focuses only on extreme curves. The new coefficient is derived within the framework of regular variation in Banach spaces. A consistent estimator is proposed and justified by an asymptotic analysis and a simulation study. The usefulness of the new coefficient is illustrated on financial and and climate functional data.
Cite
@article{arxiv.2405.17318,
title = {Extremal correlation coefficient for functional data},
author = {Mihyun Kim and Piotr Kokoszka},
journal= {arXiv preprint arXiv:2405.17318},
year = {2025}
}