Principal Component Analysis for Max-Stable Distributions

• 成果类型: Article; Early Access
• 署名作者: Reinbott, Felix; Janssen, Anja
• 署名单位: Otto von Guericke University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2025.2595732
• 发表日期: 2026-02-16
• 关键词: dimension reduction; extreme value statistics; Max-stable distributions; Principal Component Analysis; Dimension Reduction; spectral measure; dependence; extremes

摘要

Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme value distributions have turned out to provide challenges for the application of PCA since their constraint support impedes the detection of lower-dimensional structures and heavy-tails can imply that second moments do not exist, thereby preventing the application of classical variance-based techniques for PCA. We adapt PCA to max-stable distributions using a regression setting and employ max-linear maps to project the random vector to a lower-dimensional space while preserving max-stability. We also provide a characterization of those distributions which allow for a perfect reconstruction from the lower-dimensional representation. Finally, we demonstrate how an optimal projection matrix can be consistently estimated and show viability in practice with a simulation study and application to a benchmark dataset. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.