Published Paper
Inserted: 15 may 2018
Last Updated: 19 aug 2024
Journal: Nonlinear Anal.
Year: 2018
Abstract:
To generalize the notion of distribution function to dimension $d\geq 2$, in some recent papers it has been proposed a concept of center-outward distribution function based on optimal transportation ideas, and the inferential properties of the corresponding center-outward quantile function have been studied. A crucial tool needed to derive the desired inferential properties is the continuity and invertibility for the center-outward quantile function outside the origin, as this ensures the existence of closed and nested quantile contours. The aim of this paper is to prove such a continuity and invertibility result.
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