We develop a statistical framework for risk estimation, inspired by the axiomatic theory of risk measures. Coherent risk estimators -- functionals of P&L samples inheriting the economic properties of risk measures -- are defined and characterized through robust representations linked to $L$-estimators. The framework provides a canonical methodology for constructing estimators with sound financial and statistical properties, unifying risk measure theory, principles for capital adequacy, and practical statistical challenges in market risk. A numerical study illustrates the approach, focusing on expected shortfall estimation under both i.i.d. and overlapping samples relevant for regulatory FRTB model applications.

翻译：受风险测度公理化理论的启发，我们发展了一套用于风险估计的统计框架。相干风险估计量——即继承风险测度经济特性的损益样本泛函——通过关联于$L$估计量的稳健表示被定义和刻画。该框架提供了一种构建兼具稳健金融与统计特性估计量的规范方法，统一了风险测度理论、资本充足性原则以及市场风险中的实际统计挑战。数值研究通过聚焦于独立同分布样本和重叠样本下的期望短缺估计（与监管FRTB模型应用相关）阐释了该方法。