Estimation of the multivariate conditional tail expectation for extreme risk levels: Illustration on environmental data sets

Abstract

AbstractThis paper deals with the problem of estimating the multivariate version of the conditional tail expectation introduced in the recent literature. We propose a new semiparametric estimator for this risk measure, essentially based on statistical extrapolation techniques, well designed for extreme risk lev els. We prove a central limit theorem for the obtained estimator. We illustrate the practical properties of our estimator on simulations. The performances of our new estimator are discussed and compared with the ones of the empirical Kendall's process‐based estimator, previously proposed by the authors. 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 northwest of France.