• Bernoulli
  • Volume 21, Number 2 (2015), 957-1001.

Estimating failure probabilities

Holger Drees and Laurens de Haan

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In risk management, often the probability must be estimated that a random vector falls into an extreme failure set. In the framework of bivariate extreme value theory, we construct an estimator for such failure probabilities and analyze its asymptotic properties under natural conditions. It turns out that the estimation error is mainly determined by the accuracy of the statistical analysis of the marginal distributions if the extreme value approximation to the dependence structure is at least as accurate as the generalized Pareto approximation to the marginal distributions. Moreover, we establish confidence intervals and briefly discuss generalizations to higher dimensions and issues arising in practical applications as well.

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Bernoulli, Volume 21, Number 2 (2015), 957-1001.

First available in Project Euclid: 21 April 2015

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asymptotic normality exceedance probability failure set homogeneity multivariate extremes out of sample extrapolation peaks over threshold


Drees, Holger; de Haan, Laurens. Estimating failure probabilities. Bernoulli 21 (2015), no. 2, 957--1001. doi:10.3150/13-BEJ594.

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