Assessing conditional tail risk at very high or low levels is of great interest in numerous applications. Due to data sparsity in high tails, the widely used quantile regression method can suffer from high variability at the tails, especially for heavy-tailed distributions. As an alternative to quantile regression, expectile regression, which relies on the minimization of the asymmetric l2-norm and is more sensitive to the magnitudes of extreme losses than quantile regression, is considered. In this article, we develop a new estimation method for high conditional tail risk by first estimating the intermediate conditional expectiles in regression framework, and then estimating the underlying tail index via weighted combinations of the top order conditional expectiles. The resulting conditional tail index estimators are then used as the basis for extrapolating these intermediate conditional expectiles to high tails based on reasonable assumptions on tail behaviors. Finally, we use these high conditional tail expectiles to estimate alternative risk measures such as the Value at Risk (VaR) and Expected Shortfall (ES), both in high tails. The asymptotic properties of the proposed estimators are investigated. Simulation studies and real data analysis show that the proposed method outperforms alternative approaches.

在很多应用中，非常有必要评估有条件的尾巴风险很高或很低的水平。由于高尾部的数据稀疏性，因此广泛使用的分位数回归方法可能会在尾部出现高可变性，尤其是对于重尾分布。作为分位数回归的替代方法，期望回归是依赖于不对称l 2的最小化-范数，并且比分位数回归对极端损失的幅度更为敏感。在本文中，我们首先通过在回归框架中估计中间条件性的种群，然后通过加权有条件的期望性种群的加权组合，来估算潜在的条件性尾巴指数，从而开发出一种新的高条件性条件性尾巴风险估计方法。然后，根据对尾部行为的合理假设，将所得的条件尾部索引估计量用作将这些中间条件性期望值外推到高尾部的基础。最后，我们使用这些高条件的尾部期望值来估计高尾部中的替代风险度量，例如风险价值（VaR）和预期不足（ES）。研究了所提出估计量的渐近性质。