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[DP14] Estimation of Multivariate Conditional Tail Expectation using Kendall's Process
Revue Internationale avec comité de lecture : Journal Journal of Nonparametric Statistics, vol. 26(2 ), pp. 241-267, 2014, (doi:10.1080/10485252.2014.889137)
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Résumé:
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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msdma
BibTeX
| @article { | |||
| DP14, | |||
| title | = | "{Estimation of Multivariate Conditional Tail Expectation using Kendall's Process}", | |
| author | = | "E. Di Bernardino and C. Prieur", | |
| journal | = | "Journal of Nonparametric Statistics", | |
| year | = | 2014, | |
| volume | = | 26, | |
| number | = | 2 , | |
| pages | = | "241-267", | |
| doi | = | "10.1080/10485252.2014.889137", | |
| } | |||
