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Modelling the distribution for the cluster maxima of exceedances of sub-asymptotic thresholds.

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Modelling the distribution for the cluster maxima of exceedances of sub-asymptotic thresholds. / Eastoe, Emma F.; Tawn, Jon.
In: Biometrika, Vol. 99, No. 1, 03.2012, p. 43-55.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Eastoe, EF & Tawn, J 2012, 'Modelling the distribution for the cluster maxima of exceedances of sub-asymptotic thresholds.', Biometrika, vol. 99, no. 1, pp. 43-55. https://doi.org/10.1093/biomet/asr078

APA

Eastoe, E. F., & Tawn, J. (2012). Modelling the distribution for the cluster maxima of exceedances of sub-asymptotic thresholds. Biometrika, 99(1), 43-55. https://doi.org/10.1093/biomet/asr078

Vancouver

Eastoe EF, Tawn J. Modelling the distribution for the cluster maxima of exceedances of sub-asymptotic thresholds. Biometrika. 2012 Mar;99(1):43-55. doi: 10.1093/biomet/asr078

Author

Eastoe, Emma F. ; Tawn, Jon. / Modelling the distribution for the cluster maxima of exceedances of sub-asymptotic thresholds. In: Biometrika. 2012 ; Vol. 99, No. 1. pp. 43-55.

Bibtex

@article{5b45e85920e445a1948c595582b38799,
title = "Modelling the distribution for the cluster maxima of exceedances of sub-asymptotic thresholds.",
abstract = "A standard approach to model the extreme values of a stationaryprocess is the peaks over threshold method, which consists of imposinga high threshold, identifying clusters of exceedances of thisthreshold, and fitting the maximum value from each cluster using thegeneralised Pareto distribution. This approach is strongly justifiedby underlying asymptotic theory. We propose an alternative model forthe distribution of the cluster maxima which accounts for thesub-asymptotic theory of extremes of a stationary process. This newdistribution is a product of two terms, one for the marginaldistribution of exceedances and the other for the dependence structureof the exceedance values within a cluster. We illustrate theimprovement in fit, measured by the root mean square error of theestimated quantiles, offered by the new distribution over the peaksover thresholds analysis using simulated and hydrological data, and wesuggest a diagnostic tool to help identify when the proposed model islikely to lead to such an improvement in fit. ",
keywords = "cluster maxima, extremal index, generalised Pareto distribution, L-moments, peaks over thresholds",
author = "Eastoe, {Emma F.} and Jon Tawn",
year = "2012",
month = mar,
doi = "10.1093/biomet/asr078",
language = "English",
volume = "99",
pages = "43--55",
journal = "Biometrika",
issn = "1464-3510",
publisher = "Oxford University Press",
number = "1",

}

RIS

TY - JOUR

T1 - Modelling the distribution for the cluster maxima of exceedances of sub-asymptotic thresholds.

AU - Eastoe, Emma F.

AU - Tawn, Jon

PY - 2012/3

Y1 - 2012/3

N2 - A standard approach to model the extreme values of a stationaryprocess is the peaks over threshold method, which consists of imposinga high threshold, identifying clusters of exceedances of thisthreshold, and fitting the maximum value from each cluster using thegeneralised Pareto distribution. This approach is strongly justifiedby underlying asymptotic theory. We propose an alternative model forthe distribution of the cluster maxima which accounts for thesub-asymptotic theory of extremes of a stationary process. This newdistribution is a product of two terms, one for the marginaldistribution of exceedances and the other for the dependence structureof the exceedance values within a cluster. We illustrate theimprovement in fit, measured by the root mean square error of theestimated quantiles, offered by the new distribution over the peaksover thresholds analysis using simulated and hydrological data, and wesuggest a diagnostic tool to help identify when the proposed model islikely to lead to such an improvement in fit.

AB - A standard approach to model the extreme values of a stationaryprocess is the peaks over threshold method, which consists of imposinga high threshold, identifying clusters of exceedances of thisthreshold, and fitting the maximum value from each cluster using thegeneralised Pareto distribution. This approach is strongly justifiedby underlying asymptotic theory. We propose an alternative model forthe distribution of the cluster maxima which accounts for thesub-asymptotic theory of extremes of a stationary process. This newdistribution is a product of two terms, one for the marginaldistribution of exceedances and the other for the dependence structureof the exceedance values within a cluster. We illustrate theimprovement in fit, measured by the root mean square error of theestimated quantiles, offered by the new distribution over the peaksover thresholds analysis using simulated and hydrological data, and wesuggest a diagnostic tool to help identify when the proposed model islikely to lead to such an improvement in fit.

KW - cluster maxima, extremal index, generalised Pareto distribution, L-moments, peaks over thresholds

U2 - 10.1093/biomet/asr078

DO - 10.1093/biomet/asr078

M3 - Journal article

VL - 99

SP - 43

EP - 55

JO - Biometrika

JF - Biometrika

SN - 1464-3510

IS - 1

ER -