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A characterization of random variables with minimum \(L^ 2\)-distance. (English) Zbl 0688.62034

Summary: A complete characterization of multivariate random variables with minimum \(L^ 2\) 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 M. Knott and C. S. Smith [J. Optimization Theory Appl. 43, 39-49 (1984; Zbl 0519.60010)].

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H20 Measures of association (correlation, canonical correlation, etc.)
46A55 Convex sets in topological linear spaces; Choquet theory
90C25 Convex programming

Citations:

Zbl 0519.60010
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References:

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