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Vector quantile regression and optimal transport, from theory to numerics

Author

Listed:
  • Guillaume Carlier
  • Victor Chernozhukov
  • Gwendoline De Bie
  • Alfred Galichon

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. (2016, 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, 2021. "Vector quantile regression and optimal transport, from theory to numerics," Papers 2102.12809, arXiv.org.
    • Handle: RePEc:arx:papers:2102.12809
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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. Linjie Wang & Jean‐Paul Chavas & Jian Li, 2024. "Dynamic linkages in agricultural and energy markets: A quantile impulse response approach," Agricultural Economics, International Association of Agricultural Economists, vol. 55(4), pages 639-676, July.
    2. 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

    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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