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.

翻译：在回归框架下模拟重尾分布的模型差异性具有挑战性,传统的统计方法通常为分配模型设置条件,以便利学习程序。然而,这些条件可能忽略尾巴和共差之间的复杂依赖结构。此外,尾部区域的数据宽度也使推论方法不那么稳定,导致极端相关数量的估计偏差。本文建议采用梯度推动算法,以估计具有多种极端特征的功能极端值指数。我们提议的算法是一种数据驱动程序,它捕捉尾部分布的复杂和动态结构。我们还进行了广泛的模拟研究,以显示拟议算法的预测准确性。此外,我们还对真实世界数据集应用了我们的方法,以说明金融行业重尾部现象的状态和时间变化特性。