We study the consistency and weak convergence of the conditional tail function and conditional Hill estimators under broad dependence assumptions for a heavy-tailed response sequence and a covariate sequence. Consistency is established under $\alpha$-mixing, while asymptotic normality follows from $\beta$-mixing and second-order conditions. A key aspect of our approach is its versatile functional formulation in terms of the conditional tail process. Simulations demonstrate its performance across dependence scenarios. We apply our method to extreme event modeling in the oil industry, revealing distinct tail behaviors under varying conditioning values.

翻译：本研究针对重尾响应序列与协变量序列，在广泛的相依性假设下，探讨了条件尾函数与条件Hill估计量的一致性与弱收敛性。在α混合条件下建立了一致性，而渐近正态性则需基于β混合与二阶条件。本方法的核心优势在于其基于条件尾过程构建的泛函形式具有广泛适用性。数值模拟展示了该方法在不同相依场景下的性能表现。我们将该方法应用于石油行业的极端事件建模，揭示了不同条件取值下尾部行为的显著差异。