Huber loss, its asymmetric variants and their associated functionals (here named Huber functionals) are studied in the context of point forecasting and forecast evaluation. The Huber functional of a distribution is the set of minimizers of the expected (asymmetric) Huber loss, is an intermediary between a quantile and corresponding expectile, and also arises in M-estimation. Each Huber functional is elicitable, generating the precise set of minimizers of an expected score, subject to weak regularity conditions on the class of probability distributions, and has a complete characterization of its consistent scoring functions. Such scoring functions admit a mixture representation as a weighted average of elementary scoring functions. Each elementary score can be interpreted as the relative economic loss of using a particular forecast for a class of investment decisions where profits and losses are capped. The relevance of this theory for comparative assessment of weather forecasts is also discussed.

翻译：划线损失、其不对称变量及其相关功能(此处称为划线功能)在点预测和预测评价范围内研究。分配的划线功能是将预期(非对称)划线损失减到最小的一组功能,是四分位和相应预期损失之间的中间媒介,也是M估计的结果。每个划线功能都可以产生,产生预期得分的精确最小值,但概率分布等级的常规性条件不强,并完整地描述其一贯的评分功能。这种评分功能以混合表示为基本评分功能的加权平均数。每一基本得分可被解释为使用特定预测来作出某一类投资决定的相对经济损失,其中也讨论了这一理论对天气预报比较评估的相关性。