Extremal correlation coefficient for functional data

Mihyun Kim; Piotr Kokoszka

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arXiv · 2405.17318

Extremal correlation coefficient for functional data

Mihyun Kim·Piotr Kokoszka

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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.

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Mihyun Kim, Piotr Kokoszka. 2024-05-27. Extremal correlation coefficient for functional data. https://arxiv.org/abs/2405.17318

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