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Vector quantile regression and optimal transport, from theory to numerics

Author

Listed:
  • Guillaume Carlier

    (Université Paris IX Dauphine
    MOKAPLAN Inria)

  • Victor Chernozhukov

    (MIT)

  • Gwendoline De Bie

    (DMA, ENS)

  • Alfred Galichon

    (New York University)

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. "Vector quantile regression and optimal transport, from theory to numerics," Empirical Economics, Springer, vol. 62(1), pages 35-62, January.
    • Handle: RePEc:spr:empeco:v:62:y:2022:i:1:d:10.1007_s00181-020-01919-y
    DOI: 10.1007/s00181-020-01919-y
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    References listed on IDEAS

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    1. Carlier, Guillaume & Chernozhukov, Victor & Galichon, Alfred, 2017. "Vector quantile regression beyond the specified case," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 96-102.
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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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    More about this item

    Keywords

    Vector quantile regression; Optimal transport with mean independence constraints; Latent factors; Entropic regularization;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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