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Journal Articles Journal of Nonparametric Statistics Year : 2014

Estimation of Multivariate Conditional Tail Expectation using Kendall's Process

Abstract

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.
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Dates and versions

hal-00740340 , version 1 (09-10-2012)

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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⟩
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