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oai:uvadoc.uva.es:10324/824012026-03-11T08:00:00Zcom_10324_1151com_10324_931com_10324_894col_10324_1278

Barrio Tellado, Eustasio del González Sanz, Alberto Hallin, Marc 2026-01-30T11:10:18Z 2026-01-30T11:10:18Z 2020 Journal of Multivariate Analysis, Volume 180, 2020, 104671 0047-259X https://uvadoc.uva.es/handle/10324/82401 10.1016/j.jmva.2020.104671 104671 Journal of Multivariate Analysis 180 Producción Científica 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, thereby extending a recent result by Figalli [12]. Our approach relies on Cafarelli’s classical regularity theory for the solutions of the Monge-Amp`ere equation, but has to deal with difficulties related with 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 about center-outward distribution and quantile functions, including the fact that quantile sets exhibit some weak form of convexity. FEDER, Spanish Ministerio de Economía y Competitividad, Grant MTM2017-86061-C2-1-P and Junta de Castilla y León, Grants VA005P17 and VA002G18. application/pdf spa Elsevier info:eu-repo/semantics/restrictedAccess Elsevier Estadística Análisis Matemático A note on the regularity of optimal-transport-based center-outward distribution and quantile functions info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion https://www.sciencedirect.com/science/article/pii/S0047259X20302529?via%3Dihub#d1e19913 SI