Statistical functionals are called elicitable if there exists a loss or scoring function under which the functional is the optimal point forecast in expectation. While the mean and quantiles are elicitable, it has been shown in Heinrich (2014) that the mode cannot be elicited if the true distribution can follow any Lebesgue density. We strengthen this result substantially, showing that the mode cannot be elicited if the true distribution is any distribution with continuous Lebesgue density and unique local maximum. Likewise, the mode fails to be identifiable relative to this class.

翻译：如果存在一种损失或评分功能,而该功能是预期的最佳点预测,则统计功能被称为可引起。虽然中值和分数是可以引起,但海因里希(2014)中显示,如果真实分布可以跟随任何Lebesgue密度,则无法得出该模式。我们大大加强了这一结果,表明如果真实分布是连续的Lebesgue密度和独特的本地最大值的任何分布,则无法得出该模式。同样,该模式无法相对于该类别识别。