AI 中文总结
针对流数据场景下高维ES回归的离线方法依赖完整数据的缺陷，本文提出可再生估计与推断框架，模拟及保险数据集应用验证了其良好性能。
AI 中文摘要
期望短缺（ES）已成为金融与统计学中核心的一致性风险度量，高维ES回归对利用大量协变量刻画异质性尾部风险至关重要。现有高维ES回归的离线方法依赖完整数据访问，在序列批量到达、存储有限的流数据场景下失效。针对该问题，本文提出适配流数据的高维ES回归可再生估计与推断框架。通过优化仅由当前数据和历史信息确定的代理损失函数，所提方法无需存储全部原始数据即可更新ES回归系数的估计量。基于该在线估计量，本文设计了在线去偏估计量，并通过一致方差估计构建有效的Wald型置信区间。理论上，本文建立了在线高维ES估计量的非渐近误差界，验证了在线去偏估计量的渐近正态性。大量模拟实验表明，所提方法的估计精度和推断性能可与离线基准相当；在汽车保险索赔数据集上的应用，证明其在保险风险管理中具有较强实用价值。
英文摘要
Expected Shortfall (ES) has become a core coherent risk measure in finance and statistics, and high-dimensional ES regression is crucial for characterizing heterogeneous tail risk with massive covariates. Existing offline methods for high-dimensional ES regression rely on access to full data, which fails under streaming data scenarios with sequential batch arrival and limited storage. To address this issue, this paper proposes a renewable estimation and inference framework for high-dimensional ES regression tailored to streaming data. By optimizing a surrogate loss function determined only by current data and historical information, the proposed procedure updates the estimator of ES regression coefficients without storing full raw data. Based on the online estimator, we design an online debiased estimator and further construct valid Wald-type confidence intervals using consistent variance estimation. Theoretically, we establish non-asymptotic error bounds for the online high-dimensional ES estimator and verify the asymptotic normality of the online debiased estimator. Extensive simulations show that the proposed method achieves estimation accuracy and inference performance comparable to the offline benchmark. Moreover, an application on the car insurance claim dataset demonstrates strong practical value in insurance risk management.
Comments33pages,4figures
