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Reduced-Bias Estimator of the Conditional Tail Expectation of Heavy-Tailed Distributions

In: Mathematical Statistics and Limit Theorems

Author

Listed:
  • El Hadji Deme

    (Université Gaston Berger de Saint-Louis, LERSTAD)

  • Stéphane Girard

    (Inria Grenoble Rhône-Alpes & Laboratoire Jean Kuntzmann, Team Mistis)

  • Armelle Guillou

    (Université de Strasbourg & CNRS, IRMA, UMR 7501)

Abstract

Several risk measures have been proposed in the literature. In this paper, we focus on the estimation of the Conditional Tail Expectation (CTE). Its asymptotic normality has been first established in the literature under the classical assumption that the second moment of the loss variable is finite, this condition being very restrictive in practical applications. Such a result has been extended by Necir et al., (Journal of Probability and Statistics 596839:17 2010) in the case of infinite second moment. In this framework, we propose a reduced-bias estimator of the CTE. We illustrate the efficiency of our approach on a small simulation study and a real data analysis.

Suggested Citation

  • El Hadji Deme & Stéphane Girard & Armelle Guillou, 2015. "Reduced-Bias Estimator of the Conditional Tail Expectation of Heavy-Tailed Distributions," Springer Books, in: Marc Hallin & David M. Mason & Dietmar Pfeifer & Josef G. Steinebach (ed.), Mathematical Statistics and Limit Theorems, edition 127, pages 105-123, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-12442-1_7
    DOI: 10.1007/978-3-319-12442-1_7
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