AI 中文总结
针对极端条件分位数估计中的非线性与尾部外推难题，本文结合块最大值理论与广义随机森林，提出加权最大似然估计法，并证明其存在性与一致性，在模拟和股票投资组合损失数据上验证了有效性。
AI 中文摘要
估计极端条件分位数面临两大挑战：理解变量之间复杂的非线性关系，以及准确外推到数据稀疏的分布尾部。为解决这两个问题，我们提出了一种新颖的方法，将块最大值的理论框架与广义随机森林的预测能力相结合。最大值的条件分布由广义极值（GEV）分布建模，其参数依赖于协变量，并通过加权最大似然过程进行估计，权重来源于广义随机森林以捕捉复杂的高维结构。条件分位数估计量通过对估计的GEV分布函数求逆得到。我们建立了理论结果，确保所提出的加权最大似然估计量的存在性和一致性。该方法为极端分位数回归提供了一个稳健且灵活的框架。所提出方法的性能通过模拟数据以及应用于在NYSE、AMEX和NASDAQ上市的股票金融投资组合损失进行了说明。
英文摘要
Estimating extreme conditional quantiles faces two major challenges: understanding complex nonlinear relationships between variables and accurately extrapolating into the tails of the distribution, where data are sparse. To address both issues, we introduce a novel approach that combines the theoretical framework of block maxima with the predictive power of generalized random forests. The conditional distribution of maxima is modeled by a generalized extreme value (GEV) distribution whose parameters depend on the covariates and are estimated via a weighted maximum likelihood procedure, with weights derived from generalized random forests to capture complex high-dimensional structures. The conditional quantile estimator follows from the inversion of the estimated GEV distribution function. We establish theoretical results ensuring the existence and consistency of the proposed weighted maximum likelihood estimator. The method provides a robust and flexible framework for extreme quantile regression. The performance of the proposed approach is illustrated using simulated data, as well as an application to financial portfolio losses from stocks listed on the NYSE, AMEX, and NASDAQ.
Comments31 pages
