On the continuity of center-outward distribution and quantile functions

By Alessio Figalli. Nonlinear Analysis, 2018

58 citations recorded by the source corpus.

To generalize the notion of distribution function to dimension $d\geq 2$, in the recent papers it was proposed a concept of center-outward distribution function based on optimal transportation ideas, and the inferential properties of the corresponding center-outward quantile function were 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.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7c7b2d94985da51b2c194d4031622996df5ff520

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computer Vision and Pattern Recognition

In Statistics and Probability

Citations in the corpus

Distribution-Free Consistent Independence Tests via Center-Outward Ranks and Signs (2019, background): “Proposition 2.1 (Figalli 2018, Theorem 1.1; Hallin 2017, Propositions 4.1 and 4.2).”
Distribution and quantile functions, ranks and signs in dimension d: A measure transportation approach (2021, background): “That class includes the class P+d of distributions with support spt(P) = Rd considered by Hallin (2017) and Figalli (2018).”