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Extreme value theory approach to simultaneous monitoring and tresholding of multiple risk indicators

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Author Info
Einmahl, John H.J.
Li, Jun
Liu, Regina Y. (Tilburg University, Center for Economic Research)

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Abstract

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

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

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
L93 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Air Transportation

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  1. Einmahl, J.H.J. & Haan, L. de & Li, D., 2004. "Weighted approximations of tail copula processes with application to testing the multivariate extreme value condition," Discussion Paper 71, Tilburg University, Center for Economic Research. [Downloadable!]
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