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We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning.
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Empirical measures: regularity is a counter-curse to dimensionality
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Comparison between W 2 {W}_{2} distance and H ˙ − 1 \dot{H}^{−1} norm, and localization of Wasserstein distance
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Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
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Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem
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