article
On the estimation of extreme directional multivariate quantiles
Fecha
2019-01-01Registro en:
03610926
1532415X
WOS;000471392300001
SCOPUS;2-s2.0-85066618028
10.1080/03610926.2019.1619770
Autor
Torres R.
Di Bernardino E.
Laniado H.
Lillo R.E.
Institución
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.