Article
Estimation of extreme quantiles conditioning on multivariate critical layers
Author/s | Di Bernardino, Elena
Palacios Rodríguez, Fátima |
Department | Universidad de Sevilla. Departamento de Estadística e Investigación Operativa |
Publication Date | 2016-02-08 |
Deposit Date | 2024-09-20 |
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Abstract | Let 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 ... Let 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. |
Citation | Di 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. |
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