Estimation of Multivariate Conditional Tail Expectation using Kendall's Process

Elena Di Bernardino (1) , Clémentine Prieur (2)

1 CEDRIC - Centre d'études et de recherche en informatique et communications
2 MOISE - Modelling, Observations, Identification for Environmental Sciences

This paper deals with the problem of estimating the multivariate version of the Conditional-Tail-Expectation, proposed by Di Bernardino et al. [(2013), "Plug-in Estimation of Level Sets in a Non-Compact Setting with Applications in Multivariable Risk Theory", ESAIM: Probability and Statistics, (17), 236-256]. We propose a new nonparametric estimator for this multivariate risk-measure, which is essentially based on Kendall's process [Genest and Rivest, (1993), "Statistical Inference Procedures for Bivariate Archimedean Copulas", Journal of American Statistical Association, 88(423), 1034-1043]. Using the central limit theorem for Kendall's process, proved by Barbe et al. [(1996), "On Kendall's Process", Journal of Multivariate Analysis, 58(2), 197-229], we provide a functional central limit theorem for our estimator. We illustrate the practical properties of our nonparametric estimator on simulations and on two real test cases. We also propose a comparison study with the level sets-based estimator introduced in Di Bernardino et al. [(2013), "Plug-In Estimation of Level Sets in A Non-Compact Setting with Applications in Multivariable Risk Theory", ESAIM: Probability and Statistics, (17), 236-256] and with (semi-)parametric approaches.

Mots clés: Kendall's process; Multidimensional risk measures; Multivariate Kendall distribution

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Elena Di Bernardino, Clémentine Prieur. Estimation of Multivariate Conditional Tail Expectation using Kendall's Process. Journal of Nonparametric Statistics, 2014, 26 (2), pp.241-267. ⟨10.1080/10485252.2014.889137⟩. ⟨hal-00740340⟩