Fissler, Tobias; Ziegel, Johanna F. (2019). Ordersensitivity and equivariance of scoring functions. Electronic journal of statistics, 13(1), pp. 11661211. Institute of Mathematical Statistics 10.1214/19EJS1552

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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 acertain 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 Mestimation. Usually strictly consistent scoring functions for an elicitable functional are notunique. To give guidance on the choice of a scoring function, this paper introduces two additional quality criteria. Ordersensitivity 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 vectorvalued functionals, e.g. the pair (mean, variance) or (Valueat Risk, Expected Shortfall).
Item Type: 
Journal Article (Original Article) 

Division/Institute: 
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science 
UniBE Contributor: 
Fissler, Tobias and Ziegel, Johanna F. 
Subjects: 
500 Science > 510 Mathematics 
ISSN: 
19357524 
Publisher: 
Institute of Mathematical Statistics 
Language: 
English 
Submitter: 
Johanna FasciatiZiegel 
Date Deposited: 
17 Feb 2020 15:41 
Last Modified: 
17 Feb 2020 15:41 
Publisher DOI: 
10.1214/19EJS1552 
BORIS DOI: 
10.7892/boris.140203 
URI: 
https://boris.unibe.ch/id/eprint/140203 