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BY 4.0 license Open Access Published by De Gruyter Open Access October 1, 2020

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

  • Carole Bernard EMAIL logo and Alfred Müller
From the journal Dependence Modeling


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.

MSC 2010: 60E05; 60E15; 62C05; 62E10; 62E15


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Received: 2020-04-24
Accepted: 2020-09-05
Published Online: 2020-10-01

© 2020 Carole Bernard et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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