Order-sensitivity and equivariance of scoring functions

Fissler, Tobias; Ziegel, Johanna F. (2019). Order-sensitivity and equivariance of scoring functions. Electronic journal of statistics, 13(1), pp. 1166-1211. Institute of Mathematical Statistics 10.1214/19-EJS1552

[img]
Preview
Text
FisslerZiegel2019.pdf - Published Version
Available under License Creative Commons: Attribution (CC-BY).

Download (547kB) | Preview

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 M-estimation. 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. Order-sensitivity opens the pos-sibility 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 (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:

1935-7524

Publisher:

Institute of Mathematical Statistics

Language:

English

Submitter:

Johanna Fasciati-Ziegel

Date Deposited:

17 Feb 2020 15:41

Last Modified:

17 Feb 2020 15:41

Publisher DOI:

10.1214/19-EJS1552

BORIS DOI:

10.7892/boris.140203

URI:

https://boris.unibe.ch/id/eprint/140203

Actions (login required)

Edit item Edit item
Provide Feedback