Structure learning for extremal tree models

• 成果类型: Article
• 署名作者: Engelke, Sebastian; Volgushev, Stanislav
• 署名单位: University of Geneva; University of Toronto; University of Geneva
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12556
• 发表日期: 2022
• 页码: 2055-2087
• 关键词: conditional-independence; m-estimator; MULTIVARIATE; dependence; distributions; simulation

摘要

Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the important case of tree models, we develop a data-driven methodology for learning the graphical structure. We show that sample versions of the extremal correlation and a new summary statistic, which we call the extremal variogram, can be used as weights for a minimum spanning tree to consistently recover the true underlying tree. Remarkably, this implies that extremal tree models can be learned in a completely non-parametric fashion by using simple summary statistics and without the need to assume discrete distributions, existence of densities or parametric models for bivariate distributions.