Point forecasting and forecast evaluation with generalized Huber loss

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