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Elliptical Multiple Output Quantile Regression and Convex Optimization

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  • Marc Hallin
  • Miroslav Šiman

Abstract

This article extends linear quantile regression to an elliptical multiple-output regression setup. The definition of the proposed concept leads to a convex optimization problem. Its elementary properties, and the consistency of its sample counterpart, are investigated. An empirical application is provided.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Marc Hallin & Miroslav Šiman, 2015. "Elliptical Multiple Output Quantile Regression and Convex Optimization," Working Papers ECARES ECARES 2015-47, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2013/221191
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    References listed on IDEAS

    as
    1. 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.
    2. Daniel Hlubinka & Miroslav Šiman, 2015. "On generalized elliptical quantiles in the nonlinear quantile regression setup," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 249-264, June.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    4. Paindaveine, Davy, 2008. "A canonical definition of shape," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2240-2247, October.
    5. Hlubinka, Daniel & Šiman, Miroslav, 2013. "On elliptical quantiles in the quantile regression setup," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 163-171.
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    Cited by:

    1. Victor Chernozhukov & Christian Hansen & Kaspar Wuthrich, 2020. "Instrumental Variable Quantile Regression," Papers 2009.00436, arXiv.org.
    2. Marc Hallin & Miroslav Šiman, 2016. "Multiple-Output Quantile Regression," Working Papers ECARES ECARES 2016-03, ULB -- Universite Libre de Bruxelles.

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