Dependence uncertainty bounds for the energy score and the multivariate Gini mean difference
Statistics Theory
2020-04-27 v1 Probability
Methodology
Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2004.11770,
title = {Dependence uncertainty bounds for the energy score and the multivariate Gini mean difference},
author = {Carole Bernard and Alfred Müller},
journal= {arXiv preprint arXiv:2004.11770},
year = {2020}
}