Quotation Fissler, Tobias, Ziegel, Johanna F. 2019. Order-sensitivity and equivariance of scoring functions. Electronic Journal of Statistics. 13 (1), 1166-1211.




The relative performance of competing point forecasts is usually measured in terms of loss or scoring functions. It is widely accepted that these scoring function should be strictly consistent in the sense that the expected score is minimized by the correctly specified forecast for a certain statistical functional such as the mean, median, or a certain risk measure. Thus, strict consistency opens the way to meaningful forecast comparison, but is also important in regression and M-estimation. Usually strictly consistent scoring functions for an elicitable functional are not unique. To give guidance on the choice of a scoring function, this paper introduces two additional quality criteria. Order-sensitivity opens the possibility to compare two deliberately misspecified forecasts given that the forecasts are ordered in a certain sense. On the other hand, equivariant scoring functions obey similar equivariance properties as the functional at hand – such as translation invariance or positive homogeneity. In our study, we consider scoring functions for popular functionals, putting special emphasis on vector-valued functionals, e.g. the pair (mean, variance) or (Value at Risk, Expected Shortfall).


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Publication's profile

Status of publication Published
Affiliation External
Type of publication Journal article
Journal Electronic Journal of Statistics
Citation Index SCI
WU-Journal-Rating new FIN-A, VW-C
Language English
Title Order-sensitivity and equivariance of scoring functions
Volume 13
Number 1
Year 2019
Page from 1166
Page to 1211
Reviewed? Y
URL https://projecteuclid.org/euclid.ejs/1554429627
DOI https://doi.org/10.1214/19-EJS1552
Open Access Y
Open Access Link https://projecteuclid.org/download/pdfview_1/euclid.ejs/1554429627


Fissler, Tobias (Details)
Ziegel, Johanna F. (University of Bern, Switzerland)
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