The empirical cost of optimal incomplete transportation
Probability
2013-10-04 v1
Abstract
We consider the problem of optimal incomplete transportation between the empirical measure on an i.i.d. uniform sample on the d-dimensional unit cube and the true measure. This is a family of problems lying in between classical optimal transportation and nearest neighbor problems. We show that the empirical cost of optimal incomplete transportation vanishes at rate , where n denotes the sample size. In dimension the rate is the same as in classical optimal transportation, but in low dimension it is (much) higher than the classical rate.
Keywords
Cite
@article{arxiv.1310.0924,
title = {The empirical cost of optimal incomplete transportation},
author = {Eustasio del Barrio and Carlos Matrán},
journal= {arXiv preprint arXiv:1310.0924},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AOP812 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)