Estimation of extreme quantiles conditioning on multivariate critical layers

E. Di Bernardino, F. Palacios-Rodríguez
2016 Environmetrics  
Let T i := [X i | X ∈ ∂L(α)], for i = 1, . . . , d, where X = (X 1 , . . . , 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 X and the von Mises condition for
more » ... nal 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 multivariate hydrological risks.
doi:10.1002/env.2385 fatcat:gq3jek3jubbsdbbc42njhzwkci