Abstract: We develop a statistical framework for risk estimation, inspired by the axiomatic theory of risk measures. In the first part of the talk, we will discuss the Coherent Risk Estimators (CRE), functionals of P&L samples inheriting the economic properties of risk measures, that 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. In the second part of the talk, I will present a numerical study that illustrates the CRE approach, focusing on expected shortfall estimation under both i.i.d. and overlapping samples relevant for regulatory FRTB model applications.