THE EMPIRICAL COST OF OPTIMAL INCOMPLETE TRANSPORTATION
成果类型：
Article
署名作者：
del Barrio, Eustasio; Matran, Carlos
署名单位：
Universidad de Valladolid
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/12-AOP812
发表日期：
2013
页码：
3140-3156
关键词：
摘要：
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 [0, 1](d) 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 O-P(n(-1/d)), where n denotes the sample size. In dimension d >= 3 the rate is the same as in classical optimal transportation, but in low dimension it is (much) higher than the classical rate.