Hypothesis testing for partial tail correlation in multivariate extremes

TL;DR

This paper introduces partial tail correlation for understanding extremal dependence in high-dimensional data, proposing a tail regression method and hypothesis test to identify sparse relationships among variables at their extremes.

Contribution

It develops a novel framework for partial tail correlation, extending classical regression concepts to the extreme value setting with a new inference procedure.

Findings

Effective hypothesis test for extremal dependence sparsity

Simulation results validate the proposed method

Application to Danube river network demonstrates practical utility

Abstract

Statistical modeling of high dimensional extremes remains challenging and has generally been limited to moderate dimensions. Understanding structural relationships among variables at their extreme levels is crucial both for constructing simplified models and for identifying sparsity in extremal dependence. In this paper, we introduce the notion of partial tail correlation to characterize structural relationships between pairs of variables in their tails. To this end, we propose a tail regression approach for nonnegative regularly varying random vectors and define partial tail correlation based on the regression residuals. Using an extreme analogue of the covariance matrix, we show that the resulting regression coefficients and partial tail correlations take the same form as in classical non-extreme settings. For inference, we develop a hypothesis test to explore sparsity in extremal dependence structures, and demonstrate its effectiveness through simulations and an application to the Danube river network.