A0346
Title: On asymptotic independence in higher dimensions
Authors: Vicky Fasen-Hartmann - Karlsruhe Institute of Technology (Germany) [presenting]
Bikramjit Das - Singapore University of Technology and Design (Singapore)
Abstract: In the study of extremes, the presence of asymptotic independence signifies that extreme events across multiple variables are probably less likely to occur together. Although well-understood in a bivariate context, the concept remains relatively unexplored when addressing the nuances of joint occurrence of extremes in higher dimensions. A notion of mutual asymptotic independence is proposed to capture the behavior of joint extremes in dimensions larger than two and contrast it with the classical notion of (pairwise) asymptotic independence. Furthermore, k-wise asymptotic independence is defined as a relationship between pairwise and mutual asymptotic independence. The concepts are compared using examples from Archimedean, Gaussian, and Marshall-Olkin copulas, among others. Notably, for the popular Gaussian copula, explicit conditions are provided on the correlation matrix for mutual asymptotic independence to hold; moreover, exact tail orders are computed for various tail events.
