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.

翻译：极值理论中的推断依赖于有限的极端观测数据，导致估计具有挑战性。为解决这一局限，我们提出了一种非参数模拟方案——多元极端事件谱自助法模拟程序，该方案基于多元广义帕累托分布随机向量的谱表示。与标准自助法不同，我们的方法保留了数据的联合尾部行为，并生成额外的合成极端数据，从而提高了推断的可靠性。我们通过模拟数据和真实数据，在尾部风险指标估计上验证了该方法的有效性。结果凸显了该方法在增强高维极端场景风险评估中的潜力。