Principal Component Analysis for Multivariate Extremes

2026-06-05

AI Summary

This study addresses the challenge that conventional dimensionality reduction techniques often fail to preserve critical extremal dependence structures in high-dimensional multivariate extreme value data, thereby compromising the accuracy of subsequent modeling. To overcome this limitation, the authors propose a novel method that integrates principles from extreme value theory with the conceptual framework of principal component analysis, specifically designed to retain extremal dependencies during dimensionality reduction. The proposed algorithm effectively maintains key multivariate extremal characteristics while substantially reducing dimensionality, offering a computationally efficient and statistically accurate approach for analyzing high-dimensional extreme events.

Abstract

This chapter explores ways to reduce the dimensionality of the data while preserving key information relevant to the analysis of multivariate extreme values.

Problem

• Principal Component Analysis
• Multivariate Extremes
• Dimensionality Reduction
• Extreme Value Analysis

Innovation

• Principal Component Analysis
• Multivariate Extremes
• Dimensionality Reduction
• Extreme Value Analysis
• Statistical Modeling