Non-Parametric Simulation of Multivariate Extreme Events via Spectral Bootstrap

2025/09/30 by Nisrine Madhar, Madhar, Nisrine, Juliette Legrand +3
Computer Science · #FOS: Computer and information sciences #Methodology (stat.ME) #Time Series Analysis and Forecasting

paper · doi:10.48550/arxiv.2509.26451

openalex publication_date 2025/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Inference in extreme value theory relies on a limited number of extreme observations, making estimation challenging. To address this limitation, we propose a non-parametric simulation scheme, the multivariate extreme events spectral bootstrap simulation procedure, relying on the spectral representation of multivariate generalized Pareto-distributed random vectors. Unlike standard bootstrap methods, our approach preserves the joint tail behaviour of the data and generates additional synthetic extreme data, thereby improving the reliability of inference. We demonstrate the effectiveness of our procedure on the estimation of tail risk metrics, under both simulated and real data. The results highlight the potential of this method for enhancing risk assessment in high-dimensional extreme scenarios.

Citations

• Marginal expected shortfall inference under multivariate regular variation
• Extremal Random Forests
• Dependent Conditional Value-at-Risk for Aggregate Risk Models
• Tail risk inference via expectiles in heavy-tailed time series
• Multivariate generalized Pareto distributions: parametrizations, representations, and properties
• Generative Adversarial Networks
• Statistics of extremes in hydrology
• Limiting forms of the frequency distribution of the largest or smallest member of a sample

Related

• Assessing Extreme Risk using Stochastic Simulation of Extremes
• Nonparametric Bayesian Inference on Bivariate Extremes
• High dimensional inference for extreme value indices
• Likelihood based inference for high-dimensional extreme value distributions
• Conditional extremes with graphical models