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August 2021 Scoring interval forecasts: Equal-tailed, shortest, and modal interval
Jonas R. Brehmer, Tilmann Gneiting
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Bernoulli 27(3): 1993-2010 (August 2021). DOI: 10.3150/20-BEJ1298

Abstract

We consider different types of predictive intervals and ask whether they are elicitable, that is, are unique minimizers of a loss or scoring function in expectation. The equal-tailed interval is elicitable, with a rich class of suitable loss functions, though subject to translation invariance, or positive homogeneity and differentiability, the Winkler interval score becomes a unique choice. The modal interval also is elicitable, with a sole consistent scoring function, up to equivalence. However, the shortest interval fails to be elicitable relative to practically relevant classes of distributions. These results provide guidance in interval forecast evaluation and support recent choices of performance measures in forecast competitions.

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Jonas R. Brehmer. Tilmann Gneiting. "Scoring interval forecasts: Equal-tailed, shortest, and modal interval." Bernoulli 27 (3) 1993 - 2010, August 2021. https://doi.org/10.3150/20-BEJ1298

Information

Received: 1 July 2020; Revised: 1 October 2020; Published: August 2021
First available in Project Euclid: 10 May 2021

Digital Object Identifier: 10.3150/20-BEJ1298

Rights: Copyright © 2021 ISI/BS

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Vol.27 • No. 3 • August 2021
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