Sankhya A

, Volume 78, Issue 1, pp 52–86

Robust and Bias-Corrected Estimation of the Probability of Extreme Failure Sets

  • Christophe Dutang
  • Yuri Goegebeur
  • Armelle Guillou

DOI: 10.1007/s13171-015-0078-3

Cite this article as:
Dutang, C., Goegebeur, Y. & Guillou, A. Sankhya A (2016) 78: 52. doi:10.1007/s13171-015-0078-3


In multivariate extreme value statistics, the estimation of probabilities of extreme failure sets is an important problem, with practical relevance for applications in several scientific disciplines. Some estimators have been introduced in the literature, though so far the typical bias issues that arise in application of extreme value methods and the non-robustness of such methods with respect to outliers were not addressed. We introduce a bias-corrected and robust estimator for small tail probabilities. The estimator is obtained from a second order model that is fitted to properly transformed bivariate observations by means of the minimum density power divergence technique. The asymptotic properties are derived under some mild regularity conditions and the finite sample performance is evaluated through an extensive simulation study. We illustrate the practical applicability of the method on a dataset from the actuarial context.


Failure set Bias-correction Tail dependence robustness Tail quantile process. 

AMS (2000) Subject Classification

62G32 62H12 62G20 

Copyright information

© Indian Statistical Institute 2015

Authors and Affiliations

  • Christophe Dutang
    • 1
  • Yuri Goegebeur
    • 2
  • Armelle Guillou
    • 3
  1. 1.Laboratoire Manceau de MathématiqueUniversité du MaineLe MansFrance
  2. 2.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdense MDenmark
  3. 3.Institut Recherche Mathématique Avancée, UMR 7501Université de Strasbourg et CNRSStrasbourg CedexFrance

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