Geometric Criteria for Extremal Dependence Modeling

This paper introduces a geometric approach to identify and model extremal dependence in bivariate data. It leverages the shape of a limit set (characterized by a gauge function) to determine asymptotic dependence or independence. The use of additively mixed gauge functions provides a flexible modeling framework that doesn't require prior knowledge of the dependence structure, offering a computationally efficient alternative to copula models. The paper's significance lies in its novel geometric perspective and its ability to handle both asymptotic dependence and independence scenarios.

• •Proposes a geometric approach for identifying and modeling extremal dependence.
• •Uses the shape of a limit set (gauge function) to determine asymptotic dependence/independence.
• •Employs additively mixed gauge functions for flexible modeling.
• •Offers a computationally efficient alternative to copula models.
• •Handles both asymptotic dependence and independence scenarios.