Abstract
A complete characterization of multivariate random variables with minimum L2 Wasserstein-distance is proved by means of duality theory and convex analysis. This characterization allows to determine explicitly the optimal couplings for several multivariate distributions. A partial solution of this problem has been found in recent papers by Knott and Smith.
Original language | English |
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Pages (from-to) | 48-54 |
Number of pages | 7 |
Journal | Journal of Multivariate Analysis |
Volume | 32 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1990 |
Keywords
- L Wassertein-distance
- marginals
- optimal couplings
- subgradients