广义Huber损失下的点预测及预测评价
Point forecasting and forecast evaluation with generalized Huber loss
摘要：
在点预测和预测评估的背景下，研究了Huber损失、其不对称变体及其相关泛函（这里称为Huber泛函）。分布的Huber泛函是期望（非对称）Huber损失的最小化集，是分位数和相应期望值之间的中介，也出现在M估计中。每个Huber函数是可引出的，生成精确的一组期望得分的极小值，受弱正则性条件的类的概率分布，并具有完整的表征其一致的评分功能。这样的评分函数允许混合表示为基本评分函数的加权平均。每一个基本分数都可以被解释为使用特定预测的相对经济损失，用于利润和损失都有上限的一类投资决策。这一理论的相关性进行了讨论，天气预报的比较评估。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
