A1020
Title: Dimension reduction within the geometric framework for multivariate extremes
Authors: Jeongjin Lee - Lancaster University (United Kingdom) [presenting]
Abstract: The framework of geometric extremes relies on the convergence of scaled sample clouds onto a limit set, characterized by a gauge function whose shape determines the extremal dependence structure. Recent statistical methodologies for estimating the limit set provide flexibility in capturing complex dependence structure. However, existing approaches are limited to relatively low dimensions. The focus is on a statistical model comprising a truncated gamma model for the radial component, conditional on the angular component, and an angular model defined on the simplex, leading to compositional data. In high dimensions, a common dimension reduction approach is to transform the angular components and apply principal component analysis. However, this approach can inflate variation in minor components and fail to capture linear patterns in the original compositional scale. As an alternative, compositional data is analyzed, directly on its original scale, using recently proposed methods that construct a nested sequence of lower-dimensional simplices, analogous to reverse principal component analysis. The performance of these methods is evaluated and compared through simulation studies and real data applications.
