Identification and scoring functions are statistical tools to assess the calibration of risk measure estimates and to compare their performance with other estimates, e.g. in backtesting. A risk measure is called identifiable (elicitable) if it admits a strict identification function (strictly consistent scoring function). We consider measures of systemic risk introduced in Feinstein et al. (SIAM J. Financial Math. 8:672–708, 2017). Since these are set-valued, we work within the theoretical framework of Fissler et al. (preprint, available online at arXiv:1910.07912v2, 2020) for forecast evaluation of set-valued functionals. We construct oriented selective identification functions, which induce a mixture representation of (strictly) consistent scoring functions. Their applicability is demonstrated with a comprehensive simulation study.

识别和评分功能是统计工具，用于评估风险衡量估算的校准，并将其性能与其他估算（例如回测）进行比较。如果风险度量具有严格的识别功能（严格一致的评分功能），则称为可识别（可确定）。我们考虑在Feinstein等人中引入的系统性风险度量。（SIAM J. Financial Math。8：672–708，2017）。由于这些都是设定值，因此我们在Fissler等人的理论框架内工作。（预印本，在线可在arXiv：1910.07912v2，2020年获得），用于对集值功能进行预测评估。我们构造了定向的选择性识别函数，该函数诱导（严格）一致评分函数的混合表示。全面的仿真研究证明了它们的适用性。