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Some negative results on extreme multivariate quantiles defined through convex optimisation

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 : A discussion of some general properties that a notion of extreme multivariate quantile should satisfy will be given. We will then recall the concept of geometric quantile by transposing the definition of a univariate quantile as a minimiser of a cost function based on the so-called check function to the multivariate case. We shall then argue that extreme versions of these geometric quantiles are not suitable for the extreme-value analysis of a multivariate data set. A particular reason for this is that when the underlying distribution possesses a finite covariance matrix then the magnitude of these quantiles grows at a fixed rate that is independent of the distribution. We shall also discuss an extension of this negative result to the wider class of geometric M-quantiles.
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https://hal.archives-ouvertes.fr/hal-01667186
Contributor : Stephane Girard <>
Submitted on : Tuesday, December 19, 2017 - 10:48:36 AM
Last modification on : Thursday, March 26, 2020 - 8:49:32 PM

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  • HAL Id : hal-01667186, version 1

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Stéphane Girard, Gilles Stupfler. Some negative results on extreme multivariate quantiles defined through convex optimisation. 10th International Conference of the ERCIM WG on Computing and Statistics, Dec 2017, London, United Kingdom. ⟨hal-01667186⟩

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