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Estimation of multivariate conditional-tail-expectation using Kendall’s process. (English) Zbl 1359.62183

Summary: This paper deals with the problem of estimating the multivariate version of the Conditional-Tail-Expectation, proposed by E. Di Bernardino et al. [ESAIM, Probab. Stat. 17, 236–256 (2013; Zbl 06282472)]. We propose a new nonparametric estimator for this multivariate risk-measure, which is essentially based on Kendall’s process [C. Genest and L. P. Rivest, J. Am. Stat. Assoc. 88, No. 423, 1034–1043 (1993; Zbl 0785.62032)]. Using the central limit theorem for Kendall’s process, proved by P. Barbe et al. [J. Multivariate Anal. 58, No. 2, 197–229 (1996; Zbl 0862.60020)], 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., loc. cit.] and with (semi-)parametric approaches.

MSC:

62H12 Estimation in multivariate analysis
62E17 Approximations to statistical distributions (nonasymptotic)
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
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