Data from: Estimation of extreme quantiles conditioning on multivariate critical layers

Let Ti:= [Xi| X∈ ∂ L(α)], for i=1, ... ,d, where X=(X1, ... , Xd) is a risk vector and  ∂ L(α) is the associated multivariate critical layer at level α ∈ (0,1). The aim of this work is to propose a non-parametric extreme estimation procedure for the (1-pn)-quantile of Ti for a fixed α and when   pn→0, as the sample size  n→+∞. An  extrapolation method  is developed under the Archimedean copula assumption for the dependence structure of X and the von Mises condition for marginal Xi . The main result is the Central Limit Theorem for  our estimator for p=pn→0, when n tends towards infinity. A set of simulations illustrates the finite-sample performance of the proposed estimator. We finally illustrate how the proposed estimation procedure can help in the evaluation of extreme multivariatehydrological risks.