Parametric and nonparametric symmetries in graphical models for extremes

• 成果类型: Article; Early Access
• 署名作者: Rottger, Frank; Coons, Jane Ivy; Grosdos, Alexandros
• 署名单位: University of Twente; Worcester Polytechnic Institute; University of Augsburg
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412; 1467-9868
• DOI: 10.1093/jrsssb/qkag079
• 发表日期: 2026-06-02
• 关键词: coloured graphs; Graphical Models; Multivariate Extremes; parameter symmetries

摘要

Coloured graphical models provide a parsimonious approach to modeling high-dimensional data by exploiting symmetries in the model parameters. In this work, we introduce the notion of colouring for extremal graphical models on generalized multivariate Pareto distributions, a natural class of limiting distributions for threshold exceedances. Thanks to a stability property of the generalized multivariate Pareto distributions, coloured extremal tree models can be defined fully nonparametrically. For more general graphs, the parametric family of H & uuml;sler-Reiss distributions allows for two alternative approaches to coloured graphical models. We study both model classes and introduce statistical methodology for parameter estimation. It turns out that for H & uuml;sler-Reiss tree models the different definitions of coloured graphical models coincide. In addition, we show a general parametric description of extremal conditional independence statements for H & uuml;sler-Reiss distributions. Finally, we demonstrate that our methodology outperforms existing approaches on a real data set.