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Computing multiple-output regression quantile regions


  • Paindaveine, Davy
  • Šiman, Miroslav


A procedure relying on linear programming techniques is developed to compute (regression) quantile regions that have been defined recently. In the location case, this procedure allows for computing halfspace depth regions even beyond dimension two. The corresponding algorithm is described in detail, and illustrations are provided both for simulated and real data. The efficiency of a Matlab implementation of the algorithm11The code can be downloaded from is also investigated through extensive simulations.

Suggested Citation

  • Paindaveine, Davy & Šiman, Miroslav, 2012. "Computing multiple-output regression quantile regions," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 840-853.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:4:p:840-853 DOI: 10.1016/j.csda.2010.11.014

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    References listed on IDEAS

    1. Paindaveine, Davy & Siman, Miroslav, 2011. "On directional multiple-output quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 193-212, February.
    2. Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
    3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, March.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Wei, Ying, 2008. "An Approach to Multivariate Covariate-Dependent Quantile Contours With Application to Bivariate Conditional Growth Charts," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 397-409, March.
    6. Shi, Mingren & Lukas, Mark A., 2005. "Sensitivity analysis of constrained linear L1 regression: perturbations to response and predictor variables," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 779-802, April.
    7. Narula, Subhash C. & Wellington, John F., 2002. "Sensitivity analysis for predictor variables in the MSAE regression," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 355-373, August.
    8. Lukas, Mark A. & Shi, Mingren, 2006. "Sensitivity analysis of constrained linear L1 regression: Perturbations to constraints, addition and deletion of observations," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1213-1231, November.
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    Cited by:

    1. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    2. Dyckerhoff, Rainer & Mozharovskyi, Pavlo, 2016. "Exact computation of the halfspace depth," Computational Statistics & Data Analysis, Elsevier, vol. 98(C), pages 19-30.
    3. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434,, revised Sep 2015.
    4. Hlubinka, Daniel & Šiman, Miroslav, 2013. "On elliptical quantiles in the quantile regression setup," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 163-171.
    5. Marc Hallin & Miroslav Šiman, 2016. "Multiple-Output Quantile Regression," Working Papers ECARES ECARES 2016-03, ULB -- Universite Libre de Bruxelles.
    6. repec:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-016-0708-9 is not listed on IDEAS
    7. repec:spr:advdac:v:11:y:2017:i:3:d:10.1007_s11634-016-0269-3 is not listed on IDEAS
    8. repec:eee:jmvana:v:157:y:2017:i:c:p:53-69 is not listed on IDEAS
    9. repec:eee:jmvana:v:158:y:2017:i:c:p:20-30 is not listed on IDEAS
    10. Liu, Xiaohui & Zuo, Yijun & Wang, Zhizhong, 2013. "Exactly computing bivariate projection depth contours and median," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 1-11.
    11. Xiaohui Liu & Karl Mosler & Pavlo Mozharovskyi, 2017. "Fast computation of Tukey trimmed regions and median in dimension p > 2," Working Papers 2017-71, Center for Research in Economics and Statistics.


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