Estimation of extreme quantiles conditioning on multivariate critical layers

Elena Di Bernardino (1) , Fátima Palacios-Rodríguez (2)

1 CEDRIC - Centre d'études et de recherche en informatique et communications
2 Universidad de Sevilla = University of Seville

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.

Mots clés: Multivariate risk measures; extreme quantile; rainfall data-set; critical layers; Extreme Value Theory; return levels

Domaines: Statistiques [stat]

Elena Di Bernardino, Fátima Palacios-Rodríguez. Estimation of extreme quantiles conditioning on multivariate critical layers . 2016. ⟨hal-01201727v2⟩