RT info:eu-repo/semantics/article
T1 Central limit theorems for semi-discrete Wasserstein distances
A1 del Barrio, Eustasio
A1 González Sanz, Alberto
A1 Loubes, Jean-Michel
K1 Estadística
K1 Probabilidad
K1 central limit theorem , Laguerre cells , Optimal transport , optimal transport potentials , semi-discrete optimal transport
AB We prove a Central Limit Theorem for the empirical optimal transport cost, √nmn+m{Tc(Pn,Qm)−Tc(P,Q)}, in the semi-discrete case, i.e when the distribution P is supported in N points, but without assumptions on Q. We show that the asymptotic distribution is the sup of a centered Gaussian process, which is Gaussian under some additional conditions on the probability Q and on the cost. Such results imply the central limit theorem for the p-Wassertein distance, for p≥1. This means that, for fixed N, the curse of dimensionality is avoided. To better understand the influence of such N, we provide bounds of E|Wpp(P,Qm)−Wpp(P,Q)| depending on m and N. Finally, the semi-discrete framework provides a control on the second derivative of the dual formulation, which yields the first central limit theorem for the optimal transport potentials and Laguerre cells. The results are supported by simulations that help to visualize the given limits and bounds. We analyse also the cases where classical bootstrap works.
SN 1350-7265
YR 2024
FD 2024
LK https://uvadoc.uva.es/handle/10324/82397
UL https://uvadoc.uva.es/handle/10324/82397
LA spa
NO Bernoulli 30 (1) 554 - 580, February 2024
NO Producción Científica
DS UVaDOC
RD 01-feb-2026