Estimation of extreme quantiles conditioning on multivariate critical layers

Let T-i := [Xi vertical bar X is an element of partial derivative L(alpha)], for i = 1; ... , d, where X = (X-1,X- ... , X-d) is a risk vector and partial derivative L(alpha) is the associated multivariate critical layer at level alpha is an element of(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 alpha and when p(n) -> 0, as the sample size n ->infinity. An extrapolation method is developed under the Archimedean copula assumption for the dependence structure of X 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 multivariate hydrological risks. Copyright (C) 2016 John Wiley & Sons, Ltd.