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Convex weak concordance measures and their constructions
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DOI：10.1016/j.fss.2023.108841.png)
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Abstract
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Considering the framework of weak concordance measures introduced by Liebscher in 2014, we propose and study convex weak concordance measures. This class of dependence measures contains as a proper subclass the class of all convex concordance measures, introduced and studied by Mesiar et al. in 2022, and thus it also covers the well-known concordance measures as Spearman's ������ , Gini's ������ and Blomqvist's ������. The class of all convex weak concordance measures also contains, for example, Spearman's footrule ������ , which is not a concordance measure. In this paper, we first introduce basic convex weak concordance measures built in general by means of a single point (������, ������) is an element of ▽ = {(������, ������) is an element of]0 , 1[2 divide ������ >= ������} and its transpose (������, ������) only. Then, based on basic convex weak concordance measures and probability measures on the Borel subsets of ▽, two rather general constructions of convex weak concordance measures are proposed, discussed and exemplified. Inspired by Edwards et al., probability measures-based constructions are generalized to Borel measures on B(]0 , 1[2)-based constructions also allowing some infinite measures to be considered. Finally, it is shown that the presented constructions also cover the mentioned standard (convex weak) concordance measures ������ , ������ , ������,������and provide alternative formulas for them.
Keywords:
Concordance measure
Convex concordance measure
Convex weak concordance measure
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Random vector
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