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A comparison of methods for estimating the extremal index.

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A comparison of methods for estimating the extremal index. / Navarette-Ancona, Miguel A.; Tawn, Jonathan A.
In: Extremes, Vol. 3, No. 1, 03.2000, p. 5-38.

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

Harvard

Navarette-Ancona, MA & Tawn, JA 2000, 'A comparison of methods for estimating the extremal index.', Extremes, vol. 3, no. 1, pp. 5-38. https://doi.org/10.1023/A:1009993419559

APA

Navarette-Ancona, M. A., & Tawn, J. A. (2000). A comparison of methods for estimating the extremal index. Extremes, 3(1), 5-38. https://doi.org/10.1023/A:1009993419559

Vancouver

Navarette-Ancona MA, Tawn JA. A comparison of methods for estimating the extremal index. Extremes. 2000 Mar;3(1):5-38. doi: 10.1023/A:1009993419559

Author

Navarette-Ancona, Miguel A. ; Tawn, Jonathan A. / A comparison of methods for estimating the extremal index. In: Extremes. 2000 ; Vol. 3, No. 1. pp. 5-38.

Bibtex

@article{418538467bee43749e07dc6d7fbc4f9b,
title = "A comparison of methods for estimating the extremal index.",
abstract = "The extremal index, (01), is the key parameter when extending discussions of the limiting behavior of the extreme values from independent and identically distributed sequences to stationary sequences. As measures the limiting dependence of exceedances over a threshold u, as u tends to the upper endpoint of the distribution, it may not always be informative about the extremal dependence at levels of practical interest. Therefore we also consider a threshold-based extremal index, (u). We compare the performance of a range of different estimators for and (u) covering processes with < 1 and = 1. We find that the established methods for estimating actually estimate (u), so perform well only when (u) . For Markov processes, we introduce an estimator which is as good as the established methods when (u) but provides an improvement when (u) < = 1. We illustrate our methods using simulated data and daily rainfall measurements.",
keywords = "asymptotic independence - clusters - coefficient of tail dependence - extremal index - rainfalls",
author = "Navarette-Ancona, {Miguel A.} and Tawn, {Jonathan A.}",
year = "2000",
month = mar,
doi = "10.1023/A:1009993419559",
language = "English",
volume = "3",
pages = "5--38",
journal = "Extremes",
issn = "1386-1999",
publisher = "Springer Netherlands",
number = "1",

}

RIS

TY - JOUR

T1 - A comparison of methods for estimating the extremal index.

AU - Navarette-Ancona, Miguel A.

AU - Tawn, Jonathan A.

PY - 2000/3

Y1 - 2000/3

N2 - The extremal index, (01), is the key parameter when extending discussions of the limiting behavior of the extreme values from independent and identically distributed sequences to stationary sequences. As measures the limiting dependence of exceedances over a threshold u, as u tends to the upper endpoint of the distribution, it may not always be informative about the extremal dependence at levels of practical interest. Therefore we also consider a threshold-based extremal index, (u). We compare the performance of a range of different estimators for and (u) covering processes with < 1 and = 1. We find that the established methods for estimating actually estimate (u), so perform well only when (u) . For Markov processes, we introduce an estimator which is as good as the established methods when (u) but provides an improvement when (u) < = 1. We illustrate our methods using simulated data and daily rainfall measurements.

AB - The extremal index, (01), is the key parameter when extending discussions of the limiting behavior of the extreme values from independent and identically distributed sequences to stationary sequences. As measures the limiting dependence of exceedances over a threshold u, as u tends to the upper endpoint of the distribution, it may not always be informative about the extremal dependence at levels of practical interest. Therefore we also consider a threshold-based extremal index, (u). We compare the performance of a range of different estimators for and (u) covering processes with < 1 and = 1. We find that the established methods for estimating actually estimate (u), so perform well only when (u) . For Markov processes, we introduce an estimator which is as good as the established methods when (u) but provides an improvement when (u) < = 1. We illustrate our methods using simulated data and daily rainfall measurements.

KW - asymptotic independence - clusters - coefficient of tail dependence - extremal index - rainfalls

U2 - 10.1023/A:1009993419559

DO - 10.1023/A:1009993419559

M3 - Journal article

VL - 3

SP - 5

EP - 38

JO - Extremes

JF - Extremes

SN - 1386-1999

IS - 1

ER -