Estimation of directional extreme risk regions at high levels

In extreme value analysis, the focus is on the quantification of the multivariate risk outside of the observable sampling zone, which implies that a region of interest is located at high levels. This work provides an out-sample estimation method for the recently introduced Directional Multivariate Quantiles and a characterization of the risk region at high levels. The asymptotic normality of the proposed estimator is derived. Finally, the methodology is illustrated with a multivariate t-distribution for which the theoretical directional multivariate quantiles are known.