Fissler, Tobias; Ziegel, Johanna F. (2016). Higher order elicitability and Osband’s principle. Annals of statistics, 44(4), pp. 16801707. Institute of Mathematical Statistics 10.1214/16AOS1439

Text
AOS1439.pdf  Published Version Available under License Publisher holds Copyright. Download (321kB)  Preview 
A statistical functional, such as the mean or the median, is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score. Such scoring functions are called strictly consistent for the functional. The elicitability of a functional opens the possibility to compare competing forecasts and to rank them in terms of their realized scores. In this paper, we explore the notion of elicitability for multidimensional functionals and give both necessary and sufficient conditions for strictly consistent scoring functions. We cover the case of functionals with elicitable components, but we also show that onedimensional functionals that are not elicitable can be a component
of a higher order elicitable functional. In the case of the variance, this is a
known result. However, an important result of this paper is that spectral risk
measures with a spectral measure with finite support are jointly elicitable if
one adds the “correct” quantiles. A direct consequence of applied interest is
that the pair (Value at Risk, Expected Shortfall) is jointly elicitable under mild
conditions that are usually fulfilled in risk management applications.
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, Ziegel, Johanna F. 
Subjects: 
300 Social sciences, sociology & anthropology > 360 Social problems & social services 500 Science > 510 Mathematics 
ISSN: 
00905364 
Publisher: 
Institute of Mathematical Statistics 
Language: 
English 
Submitter: 
Lutz Dümbgen 
Date Deposited: 
25 Jul 2016 11:08 
Last Modified: 
05 Dec 2022 14:57 
Publisher DOI: 
10.1214/16AOS1439 
BORIS DOI: 
10.7892/boris.84467 
URI: 
https://boris.unibe.ch/id/eprint/84467 