A penalized least squares estimator for extreme-value models with multiple extreme directions
Conference
65th ISI World Statistics Congress
Format: IPS Abstract - WSC 2025
Keywords: extreme-value theory
Session: IPS 754 - Advances in High-Dimensional Extreme Value Statistics
Wednesday 8 October 10:50 a.m. - 12:30 p.m. (Europe/Amsterdam)
Abstract
When modeling a vector of risk variables, extreme scenarios are often of particular interest. Existing literature has primarily focused on cases where all risk variables become large simultaneously. To address this limitation, we examine scenarios in which distinct groups of risk variables may exhibit joint extremes while others do not — a phenomenon commonly referred to as an extreme direction. We propose a general parametric mixture model that allows any prespecified set of risk groups to define the distribution’s extreme directions. This model is constructed as a smoothed max-linear form and accommodates the full range of max-stable dependence structures. Furthermore, we introduce a penalized least-squares estimator for the model parameters, along with a data-driven procedure that simultaneously identifies groups corresponding to extreme directions and estimates the associated model parameters.