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Intriguing properties of extreme geometric quantiles

Stephane Girard 1 Gilles Stupfler 2
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP [2007-2019] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019]
Abstract : A popular way to study the tail of a distribution function is to consider its high or extreme quantiles. While this is a standard procedure for univariate distributions, it is harder for multivariate ones, primarily because there is no universally accepted definition of what a multivariate quantile should be. In this paper, we focus on extreme geometric quantiles. Their asymptotics are established, both in direction and magnitude, under suitable integrability conditions, when the norm of the associated vector tends to one. It appears that the behavior of extreme geometric quantiles is totally disconnected from the shape of the associated probability density function. As a consequence, geometric quantiles should not be used as a graphical tool for analyzing multidimensional datasets. We illustrate this phenomenon on some numerical examples.
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https://hal.inria.fr/hal-00865767
Contributor : Stephane Girard <>
Submitted on : Wednesday, September 25, 2013 - 10:03:50 AM
Last modification on : Thursday, July 9, 2020 - 9:44:36 AM
Document(s) archivé(s) le : Thursday, December 26, 2013 - 4:17:33 AM

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  • HAL Id : hal-00865767, version 1

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Stephane Girard, Gilles Stupfler. Intriguing properties of extreme geometric quantiles. 2013. ⟨hal-00865767v1⟩

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