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Extreme geometric quantiles in a multivariate regular variation framework

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Abstract

Considering extreme quantiles is a popular way to understand the tail of a distribution. While they have been extensively studied for univariate distributions, much less has been done for multivariate ones, primarily because there is no universally accepted definition of what a multivariate quantile or a multivariate distribution tail should be. In this paper, we focus on extreme geometric quantiles. In Girard and Stupfler (2015) Intriguing properties of extreme geometric quantiles, their asymptotics are established, both in direction and magnitude, under suitable integrability conditions, when the norm of the associated index vector tends to one. In this paper, we study extreme geometric quantiles when the integrability conditions are not fulfilled, in a framework of regular variation.

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Authors and Affiliations

  1. Team Mistis, Inria Grenoble Rhône-Alpes & LJK, Inovallée, 655, av. de l’Europe, Montbonnot, 38334, Saint-Ismier Cedex, France

    Stéphane Girard

  2. Aix Marseille Université, CNRS, EHESS, Centrale Marseille, GREQAM UMR 7316, 13002, Marseille, France

    Gilles Stupfler

Authors
  1. Stéphane Girard
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  2. Gilles Stupfler
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Correspondence to Stéphane Girard.

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Girard, S., Stupfler, G. Extreme geometric quantiles in a multivariate regular variation framework. Extremes 18, 629–663 (2015). https://doi.org/10.1007/s10687-015-0226-0

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  • DOI: https://doi.org/10.1007/s10687-015-0226-0

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