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We study the minimax optimal rate for estimating the Wasserstein-$1$ metric between two unknown probability measures based on $n$ i.i.d.
The speed of mean glivenko-cantelli convergence
Richard Mansfield Dudley · 1969
Earlier work this paper cites.
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H Tribel · 1980
Earlier work this paper cites.
Estimating integrated squared density derivatives: sharp best order of convergence estimates
Peter J Bickel and Yaacov Ritov · 1988
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Minimax quadratic estimation of a quadratic functional
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Some regularity properties of solutions of monge ampere equation
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The regularity of mappings with a convex potential
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Earlier work this paper cites.
Boundary regularity of maps with convex potentials–ii
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On minimax optimality of estimating the adversarial losses
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Estimation of smooth densities in wasserstein distance
Jonathan Weed and Quentin Berthet · 2019
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