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

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  • Bernard Carole

    (Department of Accounting, Law and Finance, Grenoble Ecole de Management, Grenoble, France, Faculty of Economics, Vrije Universiteit Brussel, Brussels, Belgium)

  • Müller Alfred

    (Department of Mathematics, University of Siegen, Siegen, Germany)

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.

Suggested Citation

  • Bernard Carole & Müller Alfred, 2020. "Dependence uncertainty bounds for the energy score and the multivariate Gini mean difference," Dependence Modeling, De Gruyter, vol. 8(1), pages 239-253, January.
    • Handle: RePEc:vrs:demode:v:8:y:2020:i:1:p:239-253:n:4
    DOI: 10.1515/demo-2020-0014
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    References listed on IDEAS

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    2. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    3. Shlomo Yitzhaki, 2003. "Gini’s Mean difference: a superior measure of variability for non-normal distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 285-316.
    4. Florian Ziel & Kevin Berk, 2019. "Multivariate Forecasting Evaluation: On Sensitive and Strictly Proper Scoring Rules," Papers 1910.07325, arXiv.org.
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    Cited by:

    1. Capaldo, Marco & Di Crescenzo, Antonio & Pellerey, Franco, 2024. "Generalized Gini’s mean difference through distortions and copulas, and related minimizing problems," Statistics & Probability Letters, Elsevier, vol. 206(C).

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