On the estimation of extreme directional multivariate quantiles Articles uri icon

publication date

  • May 2019

start page

  • 5504

end page

  • 5534

International Standard Serial Number (ISSN)

  • 0361-0926

Electronic International Standard Serial Number (EISSN)

  • 1532-415X


  • 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.


  • high level estimation; directional multivariate quantiles; multivariate extreme value theory; multivariate regular variation; bootstrap method