Estimating failure probabilities
Copyright policy )Estimating failure probabilities
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.
Published at http://dx.doi.org/10.3150/13-BEJ594 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
- Universität Hamburg Germany
- Erasmus University Rotterdam Netherlands
FOS: Computer and information sciences, asymptotic normality, Statistics of extreme values; tail inference, Mathematics - Statistics Theory, Statistics Theory (math.ST), marginal distributions, exceedance probability, multivariate extremes, Extreme value theory; extremal stochastic processes, Methodology (stat.ME), homogeneity, out of sample extrapolation, generalized Pareto approximation, FOS: Mathematics, failure set, extreme failure set, peaks over threshold, confidence intervals, Statistics - Methodology
FOS: Computer and information sciences, asymptotic normality, Statistics of extreme values; tail inference, Mathematics - Statistics Theory, Statistics Theory (math.ST), marginal distributions, exceedance probability, multivariate extremes, Extreme value theory; extremal stochastic processes, Methodology (stat.ME), homogeneity, out of sample extrapolation, generalized Pareto approximation, FOS: Mathematics, failure set, extreme failure set, peaks over threshold, confidence intervals, Statistics - Methodology
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