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Nonparametric Multiple-Output Center-Outward Quantile Regression

Author

Listed:
  • Eustasio del Barrio
  • Alberto González-Sanz
  • Marc Hallin

Abstract

Based on the novel concept of multivariate center-outward quantiles introduced recently in Chernozhukov et al. (2017) and Hallin et al. (2021), we are considering the problem of nonparametric multiple-output quantile regression. Our approach defines nested conditional center-outward quantile regression contours and regions with given conditional probability content irrespective of the underlying distribution; their graphs constitute nested center-outward quantile regression tubes. Empirical counterparts of these concepts are constructed, yielding interpretable empirical regions andcontours which are shown to consistently reconstruct their population versions in the Pompeiu-Hausdorff topology. Our method is entirely non-parametric and performs well in simulations including heteroskedasticity and nonlinear trends; its power as a data-analytic tool is illustrated on some real datasets.

Suggested Citation

  • Eustasio del Barrio & Alberto González-Sanz & Marc Hallin, 2022. "Nonparametric Multiple-Output Center-Outward Quantile Regression," Working Papers ECARES 2022-10, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2013/342212
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    References listed on IDEAS

    as
    1. repec:spo:wpmain:info:hdl:2441/4c5431jp6o888pdrcs0fuirl40 is not listed on IDEAS
    2. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    3. repec:hal:spmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
    4. repec:spo:wpmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
    5. Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2015. "Vector quantile regression: an optimal transport approach," CeMMAP working papers 58/15, Institute for Fiscal Studies.
    6. del Barrio, Eustasio & González-Sanz, Alberto & Hallin, Marc, 2020. "A note on the regularity of optimal-transport-based center-outward distribution and quantile functions," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    7. repec:hal:spmain:info:hdl:2441/4c5431jp6o888pdrcs0fuirl40 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Segers, Johan, 2022. "Graphical and uniform consistency of estimated optimal transport plans," LIDAM Discussion Papers ISBA 2022022, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Yang, Xuzhi & Wang, Tengyao, 2024. "Multiple-output composite quantile regression through an optimal transport lens," LSE Research Online Documents on Economics 125589, London School of Economics and Political Science, LSE Library.
    3. Sulkhan Chavleishvili & Simone Manganelli, 2024. "Forecasting and stress testing with quantile vector autoregression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 66-85, January.
    4. Marc Hallin & Hang Liu, 2022. "Center-outward Rank- and Sign-based VARMA Portmanteau Tests," Working Papers ECARES 2022-27, ULB -- Universite Libre de Bruxelles.
    5. Alberto González-Sanz & Marc Hallin & Bodhisattva Sen, 2023. "Monotone Measure-Preserving Maps in Hilbert Spaces: Existence, Uniqueness, and Stability," Working Papers ECARES 2023-10, ULB -- Universite Libre de Bruxelles.
    6. 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.
    7. Marc Hallin & H Lui & Thomas Verdebout, 2022. "Nonparametric Measure-transportation-based Methods for Directional Data," Working Papers ECARES 2022-18, ULB -- Universite Libre de Bruxelles.

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    More about this item

    Keywords

    Multiple-output regression; Center-outward quantiles; Optimal transport;
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