A new example for a proper scoring rule

TL;DR

This paper introduces a novel proper scoring rule inspired by the Anderson-Darling distance, providing a new example that enhances the understanding and application of scoring rules in probabilistic forecasting.

Contribution

The paper presents a new proper scoring rule based on the Anderson-Darling distance, expanding the set of tools for evaluating probabilistic models.

Findings

Introduces a proper scoring rule derived from Anderson-Darling distance

Provides theoretical motivation and connection to existing examples

Enhances methods for assessing probabilistic forecasts

Abstract

We give a new example for a proper scoring rule motivated by the form of Anderson--Darling distance of distribution functions and Example 5 in Brehmer and Gneiting (2020).