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

Let T_i:= [X_i| <b>X</b>∈ ∂ L(α)], for i=1, ... ,d, where <b>X</b>=(X₁, ... , X_d) 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-p_n)-quantile of T_i for a fixed α and when p_n→0, as the sample size n→+∞. An extrapolation method is developed under the Archimedean copula assumption for the dependence structure of <b>X</b> and the von Mises condition for marginal X_i . The main result is the Central Limit Theorem for our estimator for p=p_n→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.<br>