论文标题
在异质极端下估计极值指数的eviboost
EVIboost for the Estimation of Extreme Value Index under Heterogeneous Extremes
论文作者
论文摘要
在回归框架下对重尾分布进行建模异质性是具有挑战性的，经典的统计方法通常将条件放在分布模型上，以促进学习过程。但是，这些条件可能会忽略尾巴和协变量的重量之间的复杂依赖性结构。此外，尾部区域的数据稀疏性也使推理方法降低了稳定，从而导致对极度相关数量的估计很大。本文提出了一种梯度增强算法，以估计具有异质极端的功能性极值指数。我们提出的算法是一个数据驱动的过程，可在尾部分布中捕获复杂而动态的结构。我们还进行了广泛的仿真研究，以显示所提出算法的预测准确性。此外，我们将我们的方法应用于现实世界中的数据集，以说明金融行业中重尾现象的状态依赖性和时变特性。
Modeling heterogeneity on heavy-tailed distributions under a regression framework is challenging, and classical statistical methodologies usually place conditions on the distribution models to facilitate the learning procedure. However, these conditions are likely to overlook the complex dependence structure between the heaviness of tails and the covariates. Moreover, data sparsity on tail regions also makes the inference method less stable, leading to largely biased estimates for extreme-related quantities. This paper proposes a gradient boosting algorithm to estimate a functional extreme value index with heterogeneous extremes. Our proposed algorithm is a data-driven procedure that captures complex and dynamic structures in tail distributions. We also conduct extensive simulation studies to show the prediction accuracy of the proposed algorithm. In addition, we apply our method to a real-world data set to illustrate the state-dependent and time-varying properties of heavy-tail phenomena in the financial industry.
