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Improved threshold diagnostic plots for extreme value analyses

Northrop, PJ; Coleman, CL; (2014) Improved threshold diagnostic plots for extreme value analyses. Extremes , 17 (2) 289 - 303. 10.1007/s10687-014-0183-z. Green open access

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Abstract

A crucial aspect of threshold-based extreme value analyses is the level at which the threshold is set. For a suitably high threshold asymptotic theory suggests that threshold excesses may be modelled by a generalized Pareto distribution. A common threshold diagnostic is a plot of estimates of the generalized Pareto shape parameter over a range of thresholds. The aim is to select the lowest threshold above which the estimates are judged to be approximately constant, taking into account sampling variability summarized by pointwise confidence intervals. This approach doesn’t test directly the hypothesis that the underlying shape parameter is constant above a given threshold, but requires the user subjectively to combine information from many dependent estimates and confidence intervals. We develop tests of this hypothesis based on a multiple-threshold penultimate model that generalizes a two-threshold model proposed recently. One variant uses only the model fits from the traditional parameter stability plot. This is particularly beneficial when many datasets are analysed and enables assessment of the properties of the test on simulated data. We assess and illustrate these tests on river flow rate data and 72 series of significant wave heights.

Type: Article
Title: Improved threshold diagnostic plots for extreme value analyses
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s10687-014-0183-z
Publisher version: http://dx.doi.org/10.1007/s10687-014-0183-z
Language: English
Additional information: The final publication is available at Springer via http://dx.doi.org/10.1007/s10687-014-0183-z
Keywords: Extreme value theory, Generalized Pareto distribution, Score test, Likelihood ratio test, Penultimate approximation, Threshold
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1434002
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