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Functionals of Clusters of Extremes
Segers,J.J.J.
Segers,J.J.J.
Abstract
For arbitrary stationary sequences of random variables satisfying a mild mixing condition, distributional approximations are established for functionals of clusters of exceedances over a high threshold.The approximations are in terms of the distribution of the process conditionally on the event that the first variable exceeds the threshold.This conditional distribution is shown to converge to a non-trivial limit if the finite-dimensional distributions of the process are in the domain of attraction of a multivariate extreme-value distribution.In this case, therefore, limit distributions are obtained for functionals of clusters of extremes, thereby generalizing results for higher-order stationary Markov chains by S.Yun (2000), J.Appl.Probab. 37, 29 44.
Description
Pagination: 22
Date
2003
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Publisher
Econometrics
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48.pdf
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Keywords
cluster functional, extermal index, extreme-value distribution, stationary sequence, tail sequence, threshold exceedance
Citation
Segers, J J J 2003 'Functionals of Clusters of Extremes' CentER Discussion Paper, vol. 2003-48, Econometrics, Tilburg.
License
info:eu-repo/semantics/restrictedAccess