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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

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 $[0,1]^{d}$ 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.

Citation

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

Information

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

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

Subjects:
Primary: 60B10
Secondary: 05C70, 60C05

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 5 • September 2013
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