Estimation of the Multivariate Conditional-Tail-Expectation for extreme risk levels: illustrations on environmental data-sets

This paper deals with the problem of estimating the Multivariate version of the Conditional-Tail-Expectation introduced in the bivariate framework in Di Bernardino et al. [16], and generalized in Cousin and Di Bernardino [13]. We propose a new semi-parametric estimator for this risk measure, essentially based on statistical extrapolation techniques, well designed for extreme risk levels. Following Cai et al. [9], we prove a central limit theorem. We illustrate the practical properties of our estimator on simulations. The performances of our new estimator are discussed and compared to the ones of the empirical Kendall's process based estimator, previously proposed in Di Bernardino and Prieur [17]. We conclude with two applications on real data-sets: rainfall measurements recorded at three stations located in the south of Paris (France) and the analysis of strong wind gusts in the north west of France.