Extreme points of a ball about a measure with finite support
Statistics Theory
2016-03-29 v2 Probability
Statistics Theory
Abstract
We show that, for the space of Borel probability measures on a Borel subset of a Polish metric space, the extreme points of the Prokhorov, Monge-Wasserstein and Kantorovich metric balls about a measure whose support has at most n points, consist of measures whose supports have at most n+2 points. Moreover, we use the Strassen and Kantorovich-Rubinstein duality theorems to develop representations of supersets of the extreme points based on linear programming, and then develop these representations towards the goal of their efficient computation.
Keywords
Cite
@article{arxiv.1504.06745,
title = {Extreme points of a ball about a measure with finite support},
author = {Houman Owhadi and Clint Scovel},
journal= {arXiv preprint arXiv:1504.06745},
year = {2016}
}