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Daily Overview |
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OT2: Optimal Transport: Theory and Applications Location: G227 Session Chair: Stephan Eckstein Session Chair: Johannes Wiesel | |
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An ordering for the strength of functional dependence University of Salzburg, Austria We introduce a new dependence order—the conditional convex order—whose minimal and maximal elements characterize independence and perfect dependence. Moreover, it characterizes conditional independence, satisfies information monotonicity, and exhibits several invariance properties. Consequently, it is an ordering for the strength of functional dependence of a random variable Y on a random vector X . As we show, various recently studied dependence measures—including Chatterjee’s rank correlation, optimal transport-based Wasserstein correlations, and rearranged dependence measures—are increasing in this order and inherit their fundamental properties from it. We characterize the conditional convex order by the Schur order and by the concordance order, and we verify it in settings such as additive error models, the multivariate normal distribution, and various copula-based models. Our results offer a unified perspective on the behavior of dependence measures across statistical models. | |
