Di Bernardino, ElenaPalacios Rodríguez, Fátima2024-09-202024-09-202016-02-08Di Bernardino, E. y Palacios Rodríguez, F. (2016). Estimation of extreme quantiles conditioning on multivariate critical layers. Environmetrics, 27 (3), 158-168. https://doi.org/10.1002/env.2385.1180-40091099-095Xhttps://hdl.handle.net/11441/162683Let 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 multivariate hydrological risks. Copyright © 2016 John Wiley & Sons, Ltd.application/pdf39 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Multivariate risk measuresreturn levelscritical layersextreme quantileinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1002/env.2385