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Vector quantile regression beyond the specified case

Author

Listed:
  • Carlier, Guillaume
  • Chernozhukov, Victor
  • Galichon, Alfred

Abstract

This paper studies vector quantile regression (VQR), which models the dependence of a random vector with respect to a vector of explanatory variables with enough flexibility to capture the whole conditional distribution, and not only the conditional mean. The problem of vector quantile regression is formulated as an optimal transport problem subject to an additional mean-independence condition. This paper provides results on VQR beyond the specified case which had been the focus of previous work. We show that even beyond the specified case, the VQR problem still has a solution which provides a general representation of the conditional dependence between random vectors.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:161:y:2017:i:c:p:96-102
    DOI: 10.1016/j.jmva.2017.07.003
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    References listed on IDEAS

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    4. Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2015. "Vector quantile regression: an optimal transport approach," CeMMAP working papers 58/15, Institute for Fiscal Studies.
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    8. Galichon, Alfred & Henry, Marc, 2012. "Dual theory of choice with multivariate risks," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1501-1516.
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    Citations

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    Cited by:

    1. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," SciencePo Working papers Main hal-03936221, HAL.
    2. 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.
    3. Nadja Klein & Torsten Hothorn & Luisa Barbanti & Thomas Kneib, 2022. "Multivariate conditional transformation models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 116-142, March.
    4. Balcilar, Mehmet & Ozdemir, Zeynel Abidin & Ozdemir, Huseyin & Wohar, Mark E., 2020. "Transmission of US and EU Economic Policy Uncertainty Shock to Asian Economies in Bad and Good Times," IZA Discussion Papers 13274, Institute of Labor Economics (IZA).
    5. Marc Hallin, 2021. "Measure Transportation and Statistical Decision Theory," Working Papers ECARES 2021-04, ULB -- Universite Libre de Bruxelles.
    6. Donald Lien & Zijun Wang, 2019. "Quantile information share," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(1), pages 38-55, January.
    7. Alfred Galichon, 2021. "The Unreasonable Effectiveness of Optimal Transport in Economics," Working Papers hal-03936221, HAL.
    8. Alfred Galichon, 2021. "The unreasonable effectiveness of optimal transport in economics," Papers 2107.04700, arXiv.org.
    9. Hongjian Shi & Mathias Drton & Marc Hallin & Fang Han, 2023. "Semiparametrically Efficient Tests of Multivariate Independence Using Center-Outward Quadrant, Spearman, and Kendall Statistics," Working Papers ECARES 2023-03, ULB -- Universite Libre de Bruxelles.

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