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

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  • Elena Di Bernardino
  • Clémentine Prieur

Abstract

This 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.

Suggested Citation

  • Elena Di Bernardino & Clémentine Prieur, 2018. "Estimation of the multivariate conditional tail expectation for extreme risk levels: Illustration on environmental data sets," Environmetrics, John Wiley & Sons, Ltd., vol. 29(7), November.
  • Handle: RePEc:wly:envmet:v:29:y:2018:i:7:n:e2510
    DOI: 10.1002/env.2510
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    Cited by:

    1. Goegebeur, Yuri & Guillou, Armelle & Qin, Jing, 2024. "Dependent conditional tail expectation for extreme levels," Stochastic Processes and their Applications, Elsevier, vol. 171(C).
    2. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    3. Beck, Nicholas & Di Bernardino, Elena & Mailhot, Mélina, 2021. "Semi-parametric estimation of multivariate extreme expectiles," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    4. Goegebeur, Yuri & Guillou, Armelle & Ho, Nguyen Khanh Le & Qin, Jing, 2023. "A Weissman-type estimator of the conditional marginal expected shortfall," Econometrics and Statistics, Elsevier, vol. 27(C), pages 173-196.
    5. Goegebeur, Yuri & Guillou, Armelle & Ho, Nguyen Khanh Le & Qin, Jing, 2023. "Nonparametric estimation of conditional marginal excess moments," Journal of Multivariate Analysis, Elsevier, vol. 193(C).

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