分布鲁棒优化作为刻画极值分布的可扩展框架
Distributionally Robust Optimization as a Scalable Framework to Characterize Extreme Value Distributions
AI总结：
本文针对多维极值理论中极值数据稀缺导致的模型误设问题，提出结合半参数最大稳定约束的分布鲁棒优化估计器，并通过凸优化与神经网络两种实现验证了其在合成数据和金融收益数据上的有效性。
摘要：
本文的目标是开发分布鲁棒优化（DRO）估计器，特别是针对多维极值理论（EVT）统计量。EVT支持使用由空间泊松点过程构建的、称为最大稳定分布的半参数模型。这些模型虽然强大，但仅在样本量较大时渐近有效。然而，由于极值数据本质上十分稀缺，模型误设误差的可能性在这些应用中固有存在，因此DRO估计器是自然的选择。为了在提升样本外性能的同时缓解过度保守的估计，我们研究了在点过程空间中由半参数最大稳定约束所指导的DRO估计器。我们既研究了某些感兴趣问题（例如CVaR）的可处理凸形式，也研究了更一般的基于神经网络的估计器。两种方法均使用合成生成的数据进行了验证，恢复了预设特征，并验证了所提技术的有效性。此外，所提方法被应用于一个真实的金融收益数据集，并与先前分析进行了比较。我们将所提模型确立为多元EVT领域中的一种新颖表述，并且在与相关替代方案比较时在性能方面具有创新性。
英文摘要：
The goal of this paper is to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional Extreme Value Theory (EVT) statistics. EVT supports using semi-parametric models called max-stable distributions built from spatial Poisson point processes. While powerful, these models are only asymptotically valid for large samples. However, since extreme data is by definition scarce, the potential for model misspecification error is inherent to these applications, thus DRO estimators are natural. In order to mitigate over-conservative estimates while enhancing out-of-sample performance, we study DRO estimators informed by semi-parametric max-stable constraints in the space of point processes. We study both tractable convex formulations for some problems of interest (e.g. CVaR) and more general neural network based estimators. Both approaches are validated using synthetically generated data, recovering prescribed characteristics, and verifying the efficacy of the proposed techniques. Additionally, the proposed method is applied to a real data set of financial returns for comparison to a previous analysis. We established the proposed model as a novel formulation in the multivariate EVT domain, and innovative with respect to performance when compared to relevant alternate proposals.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
