Estimation of extreme quantiles conditioning on multivariate critical layers

Abstract : 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 nonparametric 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 marginal X i. The main result is the Central Limit Theorem for our estimator for p = p n → 0, as n tends towards infinity. Furthermore, using a plug-in technique, an adaptive version of the estimator is provided. A set of simulations illustrates the finite-sample performance of the proposed estimator. We conclude with an application to a rainfall data-set.
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Submitted on : Thursday, February 18, 2016 - 7:19:27 PM
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Elena Di Bernardino, Fátima Palacios-Rodríguez. Estimation of extreme quantiles conditioning on multivariate critical layers . 2016. ⟨hal-01201727v2⟩

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