Abstract
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.
Highlights
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
In recent years the so-called energy distance became a famous tool in multivariate statistics used e.g., for goodness-of- t tests and many other things
Similar concepts have been suggested in the theory of multivariate probabilistic forecasting, where the so-called energy score has been suggested as a strictly proper scoring rule for multivariate distributions in the fundamental paper of [6]
Summary
In recent years the so-called energy distance became a famous tool in multivariate statistics used e.g., for goodness-of- t tests and many other things. Gd. We rst study the corresponding dependence uncertainty bounds on the generalized expected distance between two independent d-dimensional samples from F and G. For a given observation y, we study dependence uncertainty bounds for its generalized energy score by considering inf
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