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

Author(s): Christophe Dutang, Yuri Goegebeur and Armelle Guillou
Issue: Volume 78 Series A Part 1 Year 2016
Pages: 52 -- 86
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.
AMS (2000) Subject Classification. 62G32, 62H12, 62G20.
Keywords and phrases: Failure set, Bias-correction, Tail dependence, robustness, Tail quantile process.