Wasserstein upper bounds of the total variation for smooth densities

Minwoo Chae and Stephen G. Walker

Statistics & Probability Letters, 2020, vol. 163, issue C

Abstract: 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.

Keywords: Probability inequality; Probability metric; Total variation; Sobolev space; Wasserstein metric (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2020.108771

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