### Abstract

Original language | English |
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Place of Publication | Tilburg |

Publisher | Econometrics |

Number of pages | 22 |

Volume | 2003-48 |

Publication status | Published - 2003 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2003-48 |

### Fingerprint

### Keywords

- cluster functional
- extermal index
- extreme-value distribution
- stationary sequence
- tail sequence
- threshold exceedance

### Cite this

*Functionals of Clusters of Extremes*. (CentER Discussion Paper; Vol. 2003-48). Tilburg: Econometrics.

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**Functionals of Clusters of Extremes.** / Segers, J.J.J.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Functionals of Clusters of Extremes

AU - Segers, J.J.J.

N1 - Pagination: 22

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - cluster functional

KW - extermal index

KW - extreme-value distribution

KW - stationary sequence

KW - tail sequence

KW - threshold exceedance

M3 - Discussion paper

VL - 2003-48

T3 - CentER Discussion Paper

BT - Functionals of Clusters of Extremes

PB - Econometrics

CY - Tilburg

ER -