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2021

Central Limit Theorems for General Transportation Costs

del Barrio, Eustasio, González-Sanz, Alberto, Loubes, Jean-Michel

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We consider the problem of optimal transportation with general cost between a empirical measure and a general target probability on R d , with d $\ge$ 1.

We extend results in [19] and prove asymptotic stability of both optimal transport maps and potentials for a large class of costs in R d.
We derive a central limit theorem (CLT) towards a Gaussian distribution for the empirical transportation cost under minimal assumptions, with a new proof based on the Efron-Stein inequality and on the sequential compactness of the closed unit ball in L 2 (P) for the weak topology.
We provide also CLTs for empirical Wassertsein distances in the special case of potential costs | $\bullet$ | p , p > 1.

Central Limit Theorems for General Transportation Costs · Around

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del Barrio, E., Giné, E. and Matrán, C
1999
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