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Extreme geometric quantiles in a multivariate regular variation framework

Stéphane Girard 1 Gilles Stupfler 2
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
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 (2014) "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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Stéphane Girard, Gilles Stupfler. Extreme geometric quantiles in a multivariate regular variation framework. Extremes, Springer Verlag (Germany), 2015, 18 (4), pp.629-663. ⟨10.1007/s10687-015-0226-0⟩. ⟨hal-01155112v2⟩

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