Dependence uncertainty bounds for the energy score and the multivariate Gini mean difference

• Main Authors: Bernard Carole, Müller Alfred
• Format: Article
• Language: English
• Published: De Gruyter 2020-10-01
• Series: Dependence Modeling
• Subjects: dependence uncertainty bounds; energy score; gini mean difference; spherically symmetric copula; 60e05; 60e15; 62c05; 62e10; 62e15
• Online Access: https://doi.org/10.1515/demo-2020-0014

The energy distance and energy scores became important tools in multivariate statistics and multivariate probabilistic forecasting in recent years. They are both based on the expected distance of two independent samples. In this paper we study dependence uncertainty bounds for these quantities under the assumption that we know the marginals but do not know the dependence structure. We find some interesting sharp analytic bounds, where one of them is obtained for an unusual spherically symmetric copula. These results should help to better understand the sensitivity of these measures to misspecifications in the copula.