Estimation of Multivariate Conditional Tail Expectation using Kendall's Process

International audienceThis 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)