Data from: Estimation of extreme quantiles conditioning on multivariate critical layers
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Let T<sub>i</sub>:= [X<sub>i</sub>| <b>X</b>∈ ∂ L(α)], for i=1, ... ,d, where <b>X</b>=(X<sub>1</sub>, ... , X<sub>d</sub>) 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<sub>n</sub>)-quantile of T<sub>i</sub> for a fixed α and when p<sub>n</sub>→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<sub>i</sub> . The main result is the Central Limit Theorem for our estimator for p=p<sub>n</sub>→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>
