Quantile Evaluation, Sensitivity to Bracketing, and Sharing Business Payoffs
Quantile Evaluation, Sensitivity to Bracketing, and Sharing Business Payoffs
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DOI：
10.1287/opre.2017.1588
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发表时间：
2017-05-01
影响因子：
2.7
通讯作者：
Winkler, Robert L.
中科院分区：
文献类型：
--
作者：
Grushka-Cockayne, Yael;Lichtendahl, Kenneth C., Jr.;Winkler, Robert L.
从预测竞争到有条件的风险价值要求，多重分位数评估在实践中的使用越来越多。为了评估它们，我们使用了一条来自正确评分规则的一般类别的规则，用于预测者对单个不确定的兴趣量的多个分位数。一般规则是成分分数的累加性。每个组件都包含一个函数，用于测量其分位数与实现之间的距离，并对其对总分的贡献进行加权。为了确定这一函数，我们建议，只有当预测者将实现归类时(即，他们的分位数不落在实现的同一侧)，一组的组合分位数的得分才应该好于随机选择的预测者的分位数的得分。如果一个分数满足这一性质，我们说它对括号敏感。我们刻画了一类适当的评分规则，当决策者使用广义平均来组合预测者的分位数时，这类规则对括号敏感。最后，我们将展示如何设置权重以匹配许多重要业务上下文中的收益。
From forecasting competitions to conditional value-at-risk requirements, the use of multiple quantile assessments is growing in practice. To evaluate them, we use a rule from the general class of proper scoring rules for a forecaster's multiple quantiles of a single uncertain quantity of interest. The general rule is additive in the component scores. Each component contains a function that measures its quantile's distance from the realization and weights its contribution to the overall score. To determine this function, we propose that the score of a group's combined quantile should be better than that of a randomly selected forecaster's quantile only when the forecasters bracket the realization (i.e., their quantiles do not fall on the same side of the realization). If a score satisfies this property, we say it is sensitive to bracketing. We characterize the class of proper scoring rules that is sensitive to bracketing when the decision maker uses a generalized average to combine forecasters' quantiles. Finally, we show how weights can be set to match the payoffs in many important business contexts.