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Functional, randomized and smoothed multivariate quantile regions

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  • Faugeras, Olivier P.
  • Rüschendorf, Ludger

Abstract

The mass transportation approach to multivariate quantiles in Chernozhukov et al. (2017) was modified in Faugeras and Rüschendorf (2017) by a two steps procedure. In the first step, a mass transportation problem from a spherical reference measure to the copula is solved and combined in the second step with a marginal quantile transformation in the sample space. Also, generalized quantiles given by suitable Markov morphisms are introduced there.

Suggested Citation

  • Faugeras, Olivier P. & Rüschendorf, Ludger, 2021. "Functional, randomized and smoothed multivariate quantile regions," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:jmvana:v:186:y:2021:i:c:s0047259x21000804
    DOI: 10.1016/j.jmva.2021.104802
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    References listed on IDEAS

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    1. Cuesta-Albertos, J. A. & Matrán, C. & Tuero-Diaz, A., 1997. "Optimal Transportation Plans and Convergence in Distribution," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 72-83, January.
    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. Faugeras, Olivier P., 2015. "Maximal coupling of empirical copulas for discrete vectors," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 179-186.
    4. repec:hal:spmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
    5. repec:spo:wpmain:info:hdl:2441/64itsev5509q8aa5mrbhi0g0b6 is not listed on IDEAS
    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. Rüschendorf, L. & Rachev, S. T., 1990. "A characterization of random variables with minimum L2-distance," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 48-54, January.
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