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A local moment type estimator for an extreme quantile in regression with random covariates

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  • Yuri Goegebeur
  • Armelle Guillou
  • Michael Osmann

Abstract

A conditional extreme quantile estimator is proposed in the presence of random covariates. It is based on an adaptation of the moment estimator introduced by Dekkers et al. (1989) in the classical univariate setting, and thus it is valid in the domain of attraction of the extreme value distribution, i.e., whatever the sign of the extreme value index is. Asymptotic normality of the estimator is established under suitable assumptions, and its finite sample behavior is evaluated with a small simulation study, where a comparison with an alternative estimator already proposed in the literature is provided. An illustration to a real dataset concerning the world catalogue of earthquake magnitudes is also proposed.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:1:p:319-343
    DOI: 10.1080/03610926.2014.991039
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    Cited by:

    1. 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.
    2. Stéphane Girard & Gilles Stupfler & Antoine Usseglio‐Carleve, 2022. "Nonparametric extreme conditional expectile estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 78-115, March.
    3. Takuma Yoshida, 2021. "Additive models for extremal quantile regression with Pareto-type distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 103-134, March.

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