Directional Dependence of Extreme Events

2026-04-03

AI Summary

This study addresses the directional nature of asymmetric tail dependence among variables during extreme events by proposing the first directional tail dependence measure based on conditional tail expectation. Integrating rank transformation, extreme value theory, and asymptotic statistical analysis, the method characterizes the conditional tail behavior of one variable given that another attains extreme values, thereby uncovering the dominant direction of extreme influence. Theoretical analysis and simulation experiments confirm the validity and effectiveness of the proposed approach. Applied to oceanographic data, it successfully identifies significant asymmetric extreme dependencies among key variables, offering a novel tool for causal inference in extreme risk assessment.

Technology Category

Reasoning under Uncertainty: CausalityMachine Learning: Multi-class/Multi-label Learning & Extreme ClassificationConstraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphsSecurity and Privacy: Large-scale security measurementsWeb Mining and Content Analysis: Web measurements

Abstract

This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of rank-transformed variables, thereby quantifying the behavior of one variable when the other takes extreme values. We investigate the theoretical asymptotic behavior of the associated estimator. The effectiveness of the approach is demonstrated through an extensive simulation study. In addition, we discuss the use of the proposed coefficient for the detection of causal effects in extreme events. Finally, we apply the method to an oceanographic dataset, where the results highlight the strong asymmetric nature of extreme events and identify the dominant directions of extremal influence among key oceanographic variables. As a directional measure of tail dependence, our approach provides a natural tool for exploring causal-effect relationships in extreme-value settings.

Problem

• directional dependence
• extreme events
• tail dependence
• asymmetric dependence
• causal effects

Innovation

• directional dependence
• extreme events
• tail dependence
• conditional tail expectation
• causal inference