Accurate computation of robust estimates for extremal quantiles of empirical distributions is an essential task for a wide range of applicative fields, including economic policymaking and the financial industry. Such estimates are particularly critical in calculating risk measures, such as Growth-at-Risk (GaR). % and Value-at-Risk (VaR). This work proposes a conformal framework to estimate calibrated quantiles, and presents an extensive simulation study and a real-world analysis of GaR to examine its benefits with respect to the state of the art. Our findings show that CP methods consistently improve the calibration and robustness of quantile estimates at all levels. The calibration gains are appreciated especially at extremal quantiles, which are critical for risk assessment and where traditional methods tend to fall short. In addition, we introduce a novel property that guarantees coverage under the exchangeability assumption, providing a valuable tool for managing risks by quantifying and controlling the likelihood of future extreme observations.

翻译：准确计算经验分布极端分位数的稳健估计是经济政策制定和金融行业等广泛应用领域的一项基本任务。此类估计在计算风险度量（如增长风险）时尤为关键。本研究提出了一种用于估计校准分位数的保形框架，并通过广泛的模拟研究和增长风险的实际数据分析，考察了其相对于现有技术的优势。我们的研究结果表明，保形预测方法能持续改进所有水平分位数估计的校准性和稳健性。校准效果的提升在极端分位数处尤为显著，这对风险评估至关重要，而传统方法在此往往表现不足。此外，我们引入了一种新性质，该性质在可交换性假设下保证了覆盖概率，为通过量化和控制未来极端观测值的可能性来管理风险提供了有价值的工具。