Existence and uniqueness of cyclically monotone zero-couplings are established for arbitrary pairs of infinite measures in M_0(R^d) under a Hausdorff-dimension condition, with the tail limit of such couplings for regularly varying distributions coinciding with the unique proper zero-coupling of the
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A new estimator for Monge transport maps is proposed based on Brenier potentials with convergence rates in semi-discrete settings.
Defines Wasserstein spatial depth for distributions, proves invariance and robustness properties, establishes consistency and asymptotic normality of a plug-in estimator, and supplies a two-sample test.
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Zero-couplings of infinite measures with cyclically monotone support and multivariate regular variation
Existence and uniqueness of cyclically monotone zero-couplings are established for arbitrary pairs of infinite measures in M_0(R^d) under a Hausdorff-dimension condition, with the tail limit of such couplings for regularly varying distributions coinciding with the unique proper zero-coupling of the
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Statistical Estimation of Monge Transport Maps via Brenier Potentials
A new estimator for Monge transport maps is proposed based on Brenier potentials with convergence rates in semi-discrete settings.
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Wasserstein Spatial Depth
Defines Wasserstein spatial depth for distributions, proves invariance and robustness properties, establishes consistency and asymptotic normality of a plug-in estimator, and supplies a two-sample test.