Abstract

Recent work has emphasized the importance of evaluating estimates of a statistical functional (such as a conditional mean, quantile, or distribution) using a loss function that is consistent for the functional of interest, of which there is an infinite number. If forecasters all use correctly specified models free from estimation error, and if the information sets of competing forecasters are nested, then the ranking induced by a single consistent loss function is sufficient for the ranking by any consistent loss function. This article shows, via analytical results and realistic simulation-based analyses, that the presence of misspecified models, parameter estimation error, or nonnested information sets, leads generally to sensitivity to the choice of (consistent) loss function. Thus, rather than merely specifying the target functional, which narrows the set of relevant loss functions only to the class of loss functions consistent for that functional, forecast consumers or survey designers should specify the single specific loss function that will be used to evaluate forecasts. An application to survey forecasts of U.S. inflation illustrates the results.

摘要

最近的工作强调了使用与感兴趣的函数一致的损失函数来评估统计函数（例如条件均值，分位数或分布）的估计值的重要性，该函数具有无限数量。如果预报员全部使用正确的指定模型而没有估计误差，并且如果嵌套竞争的预报员的信息集，则由单个一致损失函数引起的排名就足以由任何一致损失函数进行排名。本文通过分析结果和基于仿真的现实分析表明，指定不正确的模型，参数估计误差或非嵌套信息集的存在通常会导致对（一致）损失函数选择的敏感性。因此，不仅要指定目标功能，与该功能一致的损失函数类别，预测消费者或调查设计者应指定将用于评估预测的单个特定损失函数。一个调查美国通货膨胀预测的应用程序说明了结果。