We present a method for comparing point forecasts in a region of interest, such as the tails or centre of a variable's range. This method cannot be hedged, in contrast to conditionally selecting events to evaluate and then using a scoring function that would have been consistent (or proper) prior to event selection. Our method also gives decompositions of scoring functions that are consistent for the mean or a particular quantile or expectile. Each member of each decomposition is itself a consistent scoring function that emphasises performance over a selected region of the variable's range. The score of each member of the decomposition has a natural interpretation rooted in optimal decision theory. It is the weighted average of economic regret over user decision thresholds, where the weight emphasises those decision thresholds in the corresponding region of interest.
翻译:我们提出了一个方法,用于比较有关区域的点预测,例如变量范围的尾部或中心。这种方法无法对准,与有条件地选择用于评估的事件,然后使用在事件选择之前会一致(或适当)的评分函数相对照。我们的方法还分解了与平均值或特定孔或预期值一致的评分函数。每个分解组的每个成员本身就是一个一致的评分函数,它强调该变量范围选定区域的性能。分解的每个成员的得分都是基于最佳决策理论的自然解释,是相对于用户决定阈值的加权平均经济遗憾,而用户决定阈值的加权平均值强调在相应利益区域的决定阈值。