Open Access
September 2013 The empirical cost of optimal incomplete transportation
Eustasio del Barrio, Carlos Matrán
Ann. Probab. 41(5): 3140-3156 (September 2013). DOI: 10.1214/12-AOP812


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 $d\geq3$ the rate is the same as in classical optimal transportation, but in low dimension it is (much) higher than the classical rate.


Download Citation

Eustasio del Barrio. Carlos Matrán. "The empirical cost of optimal incomplete transportation." Ann. Probab. 41 (5) 3140 - 3156, September 2013.


Published: September 2013
First available in Project Euclid: 12 September 2013

zbMATH: 1291.60011
MathSciNet: MR3127877
Digital Object Identifier: 10.1214/12-AOP812

Primary: 60B10
Secondary: 05C70 , 60C05

Keywords: optimal incomplete transportation , optimal matching , optimal partial matching , Optimal transportation , Random quantization , rates of convergence

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 5 • September 2013
Back to Top