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On the asymptotic behaviour of extreme geometric quantiles

Gilles Stupfler 1 Stéphane Girard 2
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
Abstract : Central properties of geometric quantiles have been well-established in the recent statistical literature. In this study, we try to get a grasp of how extreme geometric quantiles behave. Their asymptotics are provided, both in direction and magnitude, under suitable moment conditions, when the norm of the associated index vector tends to one. Some intriguing properties are highlighted: in particular, it appears that if a random vector has a finite covariance matrix, then the magnitude of its extreme geometric quantiles grows at a fixed rate. The case when the random vector of interest does not have a finite covariance matrix is tackled in a multivariate regular variation framework. We illustrate our results on a simulation study.
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Submitted on : Friday, June 26, 2015 - 9:27:56 AM
Last modification on : Thursday, November 4, 2021 - 11:58:07 AM


  • HAL Id : hal-01168521, version 1


Gilles Stupfler, Stéphane Girard. On the asymptotic behaviour of extreme geometric quantiles. 9th International Conference on Extreme Value Analysis, Jun 2015, Ann Arbor, United States. ⟨hal-01168521⟩



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