Spectral Bootstrap for Non-Parametric Simulation of Multivariate Extreme Events. Application to Risk measure estimation

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 bootstrap procedure, the multivariate extreme spectral bootstrap, 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 for 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.