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A parametric registration model for warped distributions with Wasserstein’s distance

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  • Agulló-Antolín, Marina
  • Cuesta-Albertos, J.A.
  • Lescornel, Hélène
  • Loubes, Jean-Michel

Abstract

We consider a parametric deformation model for distributions. More precisely, we assume we observe J samples of random variables which are warped from an unknown distribution template. We tackle in this paper the problem of estimating the individual deformation parameters. For this, we construct a registering criterion based on the Wasserstein distance to quantify the alignment of the distributions. We prove consistency of the empirical estimators.

Suggested Citation

  • Agulló-Antolín, Marina & Cuesta-Albertos, J.A. & Lescornel, Hélène & Loubes, Jean-Michel, 2015. "A parametric registration model for warped distributions with Wasserstein’s distance," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 117-130.
    • Handle: RePEc:eee:jmvana:v:135:y:2015:i:c:p:117-130
    DOI: 10.1016/j.jmva.2014.12.005
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    References listed on IDEAS

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    1. Alvarez-Esteban, Pedro Cesar & del Barrio, Eustasio & Cuesta-Albertos, Juan Antonio & Matran, Carlos, 2008. "Trimmed Comparison of Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 697-704, June.
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    Cited by:

    1. del Barrio, Eustasio & Gordaliza, Paula & Lescornel, Hélène & Loubes, Jean-Michel, 2019. "Central limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 341-362.
    2. Rippl, Thomas & Munk, Axel & Sturm, Anja, 2016. "Limit laws of the empirical Wasserstein distance: Gaussian distributions," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 90-109.

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