On the estimation of extreme directional multivariate quantiles
Fecha
2019-01-01
Autores
Torres R.
Di Bernardino E.
Laniado H.
Lillo R.E.
Título de la revista
ISSN de la revista
Título del volumen
Editor
Marcel Dekker Inc.
Resumen
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. © 2019, © 2019 Taylor & Francis Group, LLC.