On the asymptotic behaviour of extreme geometric quantiles

Gilles Stupfler 1 Stephane Girard 2
2 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 : 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.
Type de document :
Communication dans un congrès
9th International Conference on Extreme Value Analysis, Jun 2015, Ann Arbor, United States. 2015, 9th International Conference on Extreme Value Analysis
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01168521
Contributeur : Stephane Girard <>
Soumis le : vendredi 26 juin 2015 - 09:27:56
Dernière modification le : mardi 31 janvier 2017 - 16:51:34

Identifiants

  • HAL Id : hal-01168521, version 1

Citation

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

Partager

Métriques

Consultations de la notice

199