A new example for a proper scoring rule

Abstract

We give a new example for a proper scoring rule motivated by the form of Anderson–Darling distance of distribution functions and an example of Brehmer and Gneiting.

Keywords:

• Scoring rule
• properization
• weighted Continuous Ranked Probability Scoring rule

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62C05
• 62C99

Acknowledgments

I am grateful to Jonas Brehmer for his comments to preliminary versions of the paper that helped me a lot. I thank Sándor Baran for calling my attention to the paper of Gneiting and Ranjan (2011). I would like to thank the referee for the comments that helped me to improve the paper.

Additional information

Funding

Mátyás Barczy is supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.