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Wasserstein upper bounds of the total variation for smooth densities
Jounal
STATISTICS & PROBABILITY LETTERS
Vol
163
SCI(E) 구분
Author
Minwoo Chae, Stephen G. Walker
CONTENT
The total variation distance between probability measures cannot be bounded by the Wasserstein metric in general. If we consider sufficiently smooth probability densities, however, it is possible to bound the total variation by a power of the Wasserstein distance. We provide a sharp upper bound which depends on the Sobolev norms of the densities involved. (C) 2020 Elsevier B.V. All rights reserved.