caa a22 4500 605463867 CHVBK 20210128100255.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10687-015-0226-0 doi (NATIONALLICENCE)springer-10.1007/s10687-015-0226-0 Extreme geometric quantiles in a multivariate regular variation framework [Elektronische Daten] [Stéphane Girard, Gilles Stupfler] 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 (2015) 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. Springer Science+Business Media New York, 2015 Extreme quantile nationallicence Geometric quantile nationallicence Asymptotic behavior nationallicence Multivariate regular variation nationallicence Girard Stéphane Team Mistis, Inria Grenoble Rhône-Alpes & LJK, Inovallée, 655, av. de l'Europe, 38334, Montbonnot, Saint-Ismier Cedex, France aut Stupfler Gilles Aix Marseille Université, CNRS, EHESS, Centrale Marseille, GREQAM UMR 7316, 13002, Marseille, France aut Extremes Springer US; http://www.springer-ny.com 18/4(2015-12-01), 629-663 1386-1999 18:4<629 2015 18 10687 https://doi.org/10.1007/s10687-015-0226-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10687-015-0226-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Girard Stéphane Team Mistis, Inria Grenoble Rhône-Alpes & LJK, Inovallée, 655, av. de l'Europe, 38334, Montbonnot, Saint-Ismier Cedex, France aut NATIONALLICENCE 700 1- Stupfler Gilles Aix Marseille Université, CNRS, EHESS, Centrale Marseille, GREQAM UMR 7316, 13002, Marseille, France aut NATIONALLICENCE 773 0- Extremes Springer US; http://www.springer-ny.com 18/4(2015-12-01), 629-663 1386-1999 18:4<629 2015 18 10687