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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.
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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

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    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    2. Paindaveine, Davy, 2008. "A canonical definition of shape," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2240-2247, October.
    3. 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.
    4. 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.
    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. Marc Hallin & Miroslav Šiman, 2016. "Multiple-Output Quantile Regression," Working Papers ECARES ECARES 2016-03, ULB -- Universite Libre de Bruxelles.

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