Estimation of extreme quantiles conditioning on multivariate critical layers
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 sam...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/162683 |
| Acceso en línea: | https://hdl.handle.net/11441/162683 https://doi.org/10.1002/env.2385 |
| Access Level: | acceso abierto |
| Palabra clave: | Multivariate risk measures return levels critical layers extreme quantile |
| Sumario: | 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. |
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