Higher order elicitability and Osband’s principle
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AI 根据所提供的论文材料归类：摘要明确讨论谱风险度量以及 VaR、ES 的联合预测评价，直接对应尾部风险度量方法。
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高阶可引出性与 Osband 原理
- 研究问题
- 若某个统计泛函无法单独通过期望评分唯一识别，能否将其纳入多维泛函，并据此评价风险预测？
- 方法与思路
- 作者研究多维泛函的可引出性，给出严格一致评分函数的必要与充分条件，并分析风险度量与分位数的联合可引出性。
- 材料陈述的贡献
- 摘要称，有限支撑谱测度对应的谱风险度量可与适当分位数联合引出，VaR 与 ES 的联合可引出性是其应用推论。
- 阅读关注点
- 应核对评分函数条件、谱测度有限支撑的作用，以及 VaR 与 ES 联合可引出性所需的具体条件和适用分布。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；摘要未列出具体条件，联合可引出性也不直接保证预测准确或风险管理有效。
原文摘要
A statistical functional, such as the mean or the median, is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score. Such scoring functions are called strictly consistent for the functional. The elicitability of a functional opens the possibility to compare competing forecasts and to rank them in terms of their realized scores. In this paper, we explore the notion of elicitability for multi-dimensional functionals and give both necessary and sufficient conditions for strictly consistent scoring functions. We cover the case of functionals with elicitable components, but we also show that one-dimensional functionals that are not elicitable can be a component of a higher order elicitable functional. In the case of the variance, this is a known result. However, an important result of this paper is that spectral risk measures with a spectral measure with finite support are jointly elicitable if one adds the “correct” quantiles. A direct consequence of applied interest is that the pair (Value at Risk, Expected Shortfall) is jointly elicitable under mild conditions that are usually fulfilled in risk management applications.