RT info:eu-repo/semantics/article
T1 A note on the regularity of optimal-transport-based center-outward distribution and quantile functions
A1 del Barrio, Eustasio
A1 González-Sanz, Alberto
A1 Hallin, Marc
K1 Estadística
K1 Análisis Matemático
AB We provide sufficient conditions under wich the center-outward distribution and quantile func-tions introduced in Chernozhukov et al. (2017) and Hallin (2017) are homeomorphisms, therebyextending a recent result by Figalli [12]. Our approach relies on Cafarelli’s classical regularitytheory for the solutions of the Monge-Amp`ere equation, but has to deal with difficulties relatedwith the unboundedness at the origin of the density of the spherical uniform reference measure.Our conditions are satisfied by probabillities on Euclidean space with a general (bounded or un-bounded) convex support which are not covered in [12]. We provide some additional results aboutcenter-outward distribution and quantile functions, including the fact that quantile sets exhibitsome weak form of convexity.
PB Elsevier
SN 0047-259X
YR 2020
FD 2020
LK https://uvadoc.uva.es/handle/10324/82401
UL https://uvadoc.uva.es/handle/10324/82401
LA spa
NO Journal of Multivariate Analysis, Volume 180, 2020, 104671
NO Producción Científica
DS UVaDOC
RD 30-ene-2026