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Correction to: Vector Quantile Regression and Optimal Transport, from Theory to Numerics

Author

Listed:
  • Guillaume Carlier

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres, MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales - CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique - Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique)

  • Victor Chernozhukov

    (MIT - Massachusetts Institute of Technology)

  • Gwendoline de Bie

    (DMA - Département de Mathématiques et Applications - ENS Paris - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Alfred Galichon

    (NYU - New York University [New York] - NYU - NYU System, ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper, we first revisit the Koenker and Bassett variational approach to (univariate) quantile regression, emphasizing its link with latent factor representations and correlation maximization problems. We then review the multivariate extension due to Carlier et al. (Ann Statist 44(3):1165–92, 2016,; J Multivariate Anal 161:96–102, 2017) which relates vector quantile regression to an optimal transport problem with mean independence constraints. We introduce an entropic regularization of this problem, implement a gradient descent numerical method and illustrate its feasibility on univariate and bivariate examples.

Suggested Citation

  • Guillaume Carlier & Victor Chernozhukov & Gwendoline de Bie & Alfred Galichon, 2022. "Correction to: Vector Quantile Regression and Optimal Transport, from Theory to Numerics," Post-Print hal-03896159, HAL.
    • Handle: RePEc:hal:journl:hal-03896159
    DOI: 10.1007/s00181-020-01933-0
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    Cited by:

    1. Bernd Fitzenberger & Roger Koenker & José Machado & Blaise Melly, 2022. "Economic applications of quantile regression 2.0," Empirical Economics, Springer, vol. 62(1), pages 1-6, January.

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