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On elliptical quantiles in the quantile regression setup

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  • Hlubinka, Daniel
  • Šiman, Miroslav
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    Abstract

    This article defines a meaningful concept of elliptical location quantile with the aid of quantile regression, discusses its basic properties, and suggests its extension to a general regression framework through a locally constant nonparametric approach.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12002758
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 116 (2013)
    Issue (Month): C ()
    Pages: 163-171

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    Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:163-171

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    Related research

    Keywords: Regression quantile; Elliptical quantile; Multivariate quantile; Quantile regression; Nonparametric regression;

    References

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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. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    3. Paindaveine, Davy & Šiman, Miroslav, 2012. "Computing multiple-output regression quantile regions," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 840-853.
    4. repec:cup:cbooks:9780521496032 is not listed on IDEAS
    5. Marc Hallin & Davy Paindaveine & Miroslav Šiman, 2010. "Multivariate quantiles and multiple-output regression quantiles: From L1 optimization to halfspace depth," ULB Institutional Repository 2013/127979, ULB -- Universite Libre de Bruxelles.
    6. Ella Roelant & Stefan Aelst, 2007. "An L1-type estimator of multivariate location and shape," Statistical Methods and Applications, Springer, vol. 15(3), pages 381-393, February.
    7. Davy Paindaveine & Miroslav Šiman, 2012. "Computing multiple-output regression quantile regions from projection quantiles," Computational Statistics, Springer, vol. 27(1), pages 29-49, March.
    8. Ella Roelant & Stefan Aelst & Gert Willems, 2009. "The minimum weighted covariance determinant estimator," Metrika, Springer, vol. 70(2), pages 177-204, September.
    9. Polonik, Wolfgang, 1997. "Minimum volume sets and generalized quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 69(1), pages 1-24, July.
    10. Paindaveine, Davy & Siman, Miroslav, 2011. "On directional multiple-output quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 193-212, February.
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