On the Continuity of Center-Outward Distribution and Quantile Functions
Analysis of PDEs
2018-05-15 v1 Statistics Theory
Statistics Theory
Abstract
To generalize the notion of distribution function to dimension , 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.
Cite
@article{arxiv.1805.04946,
title = {On the Continuity of Center-Outward Distribution and Quantile Functions},
author = {Alessio Figalli},
journal= {arXiv preprint arXiv:1805.04946},
year = {2018}
}