On the estimation of extreme directional multivariate quantiles

Raúl Torres (1) , Elena Di Bernardino (2, 3) , Henry Laniado (4) , Rosa Lillo (5)

1 UVa - Universidad de Valladolid [Valladolid]
2 CEDRIC - Centre d'études et de recherche en informatique et communications
3 CEDRIC - MSDMA - CEDRIC. Méthodes statistiques de data-mining et apprentissage
4 EAFIT - EAFIT University
5 UC3M - Universidad Carlos III de Madrid [Madrid]

In multivariate extreme value theory (MEVT), the focus is on analysis outside of the observable sampling zone, which implies that the region of interest is associated to high risk levels. This work provides tools to include directional notions into the MEVT, giving the opportunity to characterize the recently introduced directional multivariate quantiles (DMQ) at high levels. Then, an out-sample estimation method for these quantiles is given. A bootstrap procedure carries out the estimation of the tuning parameter in this multivariate framework and helps with the estimation of the DMQ. Asymptotic normality for the proposed estimator is provided and the methodology is illustrated with simulated data-sets. Finally, a real-life application to a financial case is also performed.

Mots clés: High level estimation; directional multivariate quantiles; multivariate extreme value theory; multivariate regular variation; bootstrap method

Domaines: Statistiques [stat]

Raúl Torres, Elena Di Bernardino, Henry Laniado, Rosa Lillo. On the estimation of extreme directional multivariate quantiles. Communications in Statistics - Theory and Methods, 2020, 49 (22), pp.5504-5534. ⟨10.1080/03610926.2019.1619770⟩. ⟨hal-04043151⟩