Sharp upper bounds are derived for the p-Wasserstein distance via discrepancy on the unit cube and via Kolmogorov-Smirnov distance times p-moments on R^d, with reverse inequalities under density conditions.
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Kolmogorov-Smirnov distance and discrepancies versus Wasserstein distances
Sharp upper bounds are derived for the p-Wasserstein distance via discrepancy on the unit cube and via Kolmogorov-Smirnov distance times p-moments on R^d, with reverse inequalities under density conditions.