Estimation of Multivariate Conditional Tail Expectation using Kendall's Process

Elena Di Bernardino 1 Clémentine Prieur 2
2 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : This paper deals with the problem of estimating the Multivariate version of the Conditional-Tail-Expectation, proposed by Cousin and Di Bernardino (2012). We propose a new non-parametric estimator for this multivariate risk-measure, which is essentially based on the Kendall's process (see Genest and Rivest, 1993). Using the Central Limit Theorem for the Kendall's process, proved by Barbe et al. (1996), we provide a functional Central Limit Theorem for our estimator. We illustrate the practical properties of our estimator on simulations. A real case in environmental framework is also analyzed. The performances of our new estimator are compared to the ones of the level sets-based estimator, previously proposed in Di Bernardino et al. (2011).
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Elena Di Bernardino, Clémentine Prieur. Estimation of Multivariate Conditional Tail Expectation using Kendall's Process. Journal of Nonparametric Statistics, American Statistical Association, 2014, 26 (2), pp.241-267. ⟨10.1080/10485252.2014.889137⟩. ⟨hal-00740340⟩

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