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On generalized elliptical quantiles in the nonlinear quantile regression setup

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  • Daniel Hlubinka
  • Miroslav Šiman

Abstract

Inspired by nonlinear quantile regression, the article introduces, investigates, discusses, and illustrates a new concept of generalized elliptical location quantiles. They may require less stringent moment assumptions, be less sensitive to outliers, be less rigid, employ more a priori information regarding the location of the distribution, and have higher potential for various regression generalizations than their common elliptical predecessor defined in the convex optimization framework by means of standard linear quantile regression. Furthermore, they still include an equivalent of their predecessor as a special case and inherit most of its favorable features such as the probability interpretation, natural equivariance properties, and good behavior for elliptical and symmetric distributions, which is demonstrated both by theoretical results and data examples with convincing graphical output. On the other hand, the new elliptical quantiles need not always be uniquely defined and they require somewhat different approach to their analysis and computation due to their intrinsically non-convex formulation. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:2:p:249-264
    DOI: 10.1007/s11749-014-0405-3
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    References listed on IDEAS

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    Cited by:

    1. Hallin, Marc & Šiman, Miroslav, 2016. "Elliptical multiple-output quantile regression and convex optimization," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 232-237.
    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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