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Extreme Value Theory Approach to Simultaneous Monitoring and Thresholding of Multiple Risk Indicators


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  • Einmahl, J.H.J.
  • Li, J.
  • Liu, R.Y.

    (Tilburg University, Center for Economic Research)


Risk assessments often encounter extreme settings with very few or no occurrences in reality.Inferences about risk indicators in such settings face the problem of insufficient data.Extreme value theory is particularly well suited for handling this type of problems.This paper uses a multivariate extreme value theory approach to establish thresholds for signaling levels of risk in the context of simultaneous monitoring of multiple risk indicators.The proposed threshold system is well justified in terms of extreme multivariate quantiles, and its sample estimator is shown to be consistent.As an illustration, the proposed approach is applied to developing a threshold system for monitoring airline performance measures.This threshold system assigns different risk levels to observed airline performance measures.In particular, it divides the sample space into regions with increasing levels of risk.Moreover, in the univariate case, such a thresholding technique can be used to determine a suitable cut-off point on a runway for holding short of landing aircrafts.This cut-off point is chosen to ensure a certain required level of safety when allowing simultaneous operations on two intersecting runways in order to ease air traffic congestion.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2006-104.

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Date of creation: 2006
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Handle: RePEc:dgr:kubcen:2006104

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Related research

Keywords: Extreme value theory; extreme quantile; multiple risk indicators; multivariate quantile; rare event; statistics of extremes; threshold system;

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  1. Einmahl, J.H.J. & Haan, L.F.M. de & Li, D., 2004. "Weighted Approximations of Tail Copula Processes with Application to Testing the Multivariate Extreme Value Condition," Discussion Paper 2004-71, Tilburg University, Center for Economic Research.
  2. Einmahl, J. & Dekkers, A. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Open Access publications from Tilburg University urn:nbn:nl:ui:12-125712, Tilburg University.
  3. Dehaan, L. & Huang, X., 1995. "Large Quantile Estimation in a Multivariate Setting," Journal of Multivariate Analysis, Elsevier, vol. 53(2), pages 247-263, May.
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