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B0209
Title: Measuring association with Wasserstein distances Authors:  Johannes Wiesel - Columbia University (United Kingdom) [presenting]
Abstract: Coupling between two probability measures on a Polish space is considered. We propose and study a class of nonparametric measures of association between these two measures. The analysis is based on the Wasserstein distance between the disintegration of the coupling with respect to the first coordinate and the marginals. 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. Throughout our analysis, we make use of the so-called adapted/causal Wasserstein distance. Our class of measures offers an alternative to the correlation coefficient. In contrast to previous works, our approach also applies to probability laws in general Polish spaces.