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Estimation of extreme conditional quantiles under a general tail-first-order condition

Author

Listed:
  • Laurent Gardes

    (Université de Strasbourg & CNRS)

  • Armelle Guillou

    (Université de Strasbourg & CNRS)

  • Claire Roman

    (Université de Strasbourg & CNRS)

Abstract

We consider the estimation of an extreme conditional quantile. In a first part, we propose a new tail condition in order to establish the asymptotic distribution of an extreme conditional quantile estimator. Next, a general class of estimators is introduced, which encompasses, among others, kernel or nearest neighbors types of estimators. A unified theorem of the asymptotic normality for this general class of estimators is provided under the new tail condition and illustrated on the different well-known examples. A comparison between different estimators belonging to this class is provided on a small simulation study and illustrated on a real dataset on earthquake magnitudes.

Suggested Citation

  • Laurent Gardes & Armelle Guillou & Claire Roman, 2020. "Estimation of extreme conditional quantiles under a general tail-first-order condition," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 915-943, August.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:4:d:10.1007_s10463-019-00713-7
    DOI: 10.1007/s10463-019-00713-7
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    References listed on IDEAS

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    1. Daouia, Abdelaati & Gardes, Laurent & Girard, Stephane, 2011. "On kernel smoothing for extremal quantile regression," LIDAM Discussion Papers ISBA 2011031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Yuri Goegebeur & Armelle Guillou & Michael Osmann, 2017. "A local moment type estimator for an extreme quantile in regression with random covariates," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(1), pages 319-343, January.
    3. Racine, Jeffrey S. & Li, Kevin, 2017. "Nonparametric conditional quantile estimation: A locally weighted quantile kernel approach," Journal of Econometrics, Elsevier, vol. 201(1), pages 72-94.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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