Papers › Measuring association with Wasserstein distances
Measuring association with Wasserstein distances
Johannes Wiesel
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Let π∈Π(μ,ν) be a coupling between two probability measures μ and ν on a Polish space. In this article we propose and study a class of nonparametric measures of association between μ and ν, which we call Wasserstein correlation coefficients. These coefficients are based on the Wasserstein distance between ν and the disintegration π_(x₁) of π with respect to the first coordinate. We also establish basic statistical properties of this new class of measures: we develop a statistical theory for strongly consistent estimators and determine their convergence rate in the case of compactly supported measures μ and ν. Throughout our analysis we make use of the so-called adapted/bicausal Wasserstein distance, in particular we rely on results established in [Backhoff, Bartl, Beiglb\"ock, Wiesel. Estimating processes in adapted Wasserstein distance. 2020]. Our approach applies to probability laws on general Polish spaces.
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