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Optimal Transportation Plans and Convergence in Distribution

Author

Listed:
  • Cuesta-Albertos, J. A.
  • Matrán, C.
  • Tuero-Diaz, A.

Abstract

Explicit expression of mappings optimal transportation plans for the Wasserstein distance in p,p>1, are not generally available. Therefore, it is of great interest to provide results which justify the practical use of simulation techniques to obtain approximate optimal transportation plans. This is done in this paper, where we obtain the consistency of the empirical optimal transportation plans. Our results can also be employed to justify a definition of multidimensional complete dependence.

Suggested Citation

  • Cuesta-Albertos, J. A. & Matrán, C. & Tuero-Diaz, A., 1997. "Optimal Transportation Plans and Convergence in Distribution," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 72-83, January.
    • Handle: RePEc:eee:jmvana:v:60:y:1997:i:1:p:72-83
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    Cited by:

    1. Faugeras, Olivier & Rüschendorf, Ludger, 2019. "Functional, randomized and smoothed multivariate quantile regions," TSE Working Papers 19-1039, Toulouse School of Economics (TSE), revised Jun 2021.
    2. Estate V. Khmaladze, 2021. "Distribution-free testing in linear and parametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1063-1087, December.
    3. Faugeras, Olivier P. & Rüschendorf, Ludger, 2021. "Functional, randomized and smoothed multivariate quantile regions," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    4. de Valk, Cees Fouad & Segers, Johan, 2018. "Stability and tail limits of transport-based quantile contours," LIDAM Discussion Papers ISBA 2018031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Florent Bonneu & Abdelaati Daouia, 2010. "Mass transportation and the consistency of the empirical optimal conditional locations," Annals of Operations Research, Springer, vol. 181(1), pages 159-170, December.
    6. J. A. Cuesta-Albertos & C. Matrán & J. Rodríguez-Rodríguez, 2003. "Approximation to Probabilities Through Uniform Laws on Convex Sets," Journal of Theoretical Probability, Springer, vol. 16(2), pages 363-376, April.
    7. Olivier Paul Faugeras & Ludger Rüschendorf, 2021. "Functional, randomized and smoothed multivariate quantile regions," Post-Print hal-03352330, HAL.

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