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Conditional Spatial Quantile: Characterization and Nonparametric Estimation

Author

Listed:
  • Mohamed CHAOUCH (IMB, Université de Bourgogne)
  • Ali GANNOUN (CNAM, Paris)
  • Jérôme SARACCO (GREThA)

Abstract

Conditional quantiles are required in various economic, biomedical or industrial problems. Lack of objective basis for ordering multivariate observations is a major problem in extending the notion of quantiles or conditional quantiles (also called regression quantiles) in a multidimensional setting. We first recall some characterizations of the unconditional spatial quantiles and the corresponding estimators. Then, we consider the conditional case. In this work, we focus our study on the geometric (or spatial) notion of quantiles introduced by Chaudhuri (1992a, 1996). We generalize, in the conditional framework, the Theorem 2.1.2 of Chaudhuri (1996), and we present algorithms allowing the calculation of the unconditional and conditional spatial quantile estimators. Finally, these various concepts are illustrated using simulated data.

Suggested Citation

  • Mohamed CHAOUCH (IMB, Université de Bourgogne) & Ali GANNOUN (CNAM, Paris) & Jérôme SARACCO (GREThA), 2008. "Conditional Spatial Quantile: Characterization and Nonparametric Estimation," Cahiers du GREThA 2008-10, Groupe de Recherche en Economie Théorique et Appliquée(GREThA).
  • Handle: RePEc:grt:wpegrt:2008-10
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    File URL: http://cahiersdugretha.u-bordeaux4.fr/2008/2008-10.pdf
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    References listed on IDEAS

    as
    1. Abdous, B. & Theodorescu, R., 1992. "Note on the spatial quantile of a random vector," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 333-336, March.
    2. Biman Chakraborty, 2001. "On Affine Equivariant Multivariate Quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 380-403, June.
    3. Robert Serfling, 2002. "Quantile functions for multivariate analysis: approaches and applications," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(2), pages 214-232, May.
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    More about this item

    Keywords

    Conditional Spatial Quantile; Contours; Kernel Estimators; Spatial Quantile;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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