The empirical cost of optimal incomplete transportation

• Autores: Eustasio del Barrio Tellado , Carlos Matrán Bea
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 5, 2013, págs. 3140-3156
• Idioma: inglés
• DOI: 10.1214/12-AOP812
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• Resumen

  • 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 OP(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.