On the indirect elicitability of the mode and modal interval
On the indirect elicitability of the mode and modal interval
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DOI：
10.1007/s10463-019-00719-1
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发表时间：
2018-04
影响因子：
1
通讯作者：
Krisztina Dearborn;Rafael M. Frongillo
中科院分区：
文献类型：
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作者：
Krisztina Dearborn;Rafael M. Frongillo
评分函数通常用于评估特定统计函数的点预测。这个评分函数应该是一致的，这意味着函数的正确值是贝叶斯行为，在这种情况下，我们说评分函数引出了函数。最近的研究结果表明，模态泛函是不可得到的。在这项工作中，我们询问是否至少有可能间接引出模态，其中可以引出一个可以计算模态的低维泛函。我们证明这是不能做到的：无论是模态还是模态区间都是相对于可识别泛函类间接引出的。
Scoring functions are commonly used to evaluate a point forecast of a particular statistical functional. This scoring function should be consistent, meaning the correct value of the functional is the Bayes act, in which case we say the scoring function elicits the functional. Recent results show that the mode functional is not elicitable. In this work, we ask whether it is at least possible to indirectly elicit the mode, wherein one elicits a low-dimensional functional from which the mode can be computed. We show that this cannot be done: Neither the mode nor a modal interval is indirectly elicitable with respect to the class of identifiable functionals.