Improved threshold diagnostic plots for extreme value analyses

Extremes volume 17, pages289–303(2014)Cite this article

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.

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Author notes

  1. Claire L. Coleman

    Present address: Pragmatic Clinical Trials Unit (PCTU), Centre for Primary Care and Public Health, Blizard Institute, Barts and The London School of Medicine & Dentistry, Yvonne Carter Building, 58 Turner Street, London, E1 2AB, UK

Affiliations

  1. Department of Statistical Science, University College London, Gower Street, London, WC1E 6BT, UK

    Paul J. Northrop & Claire L. Coleman

Authors
  1. Paul J. Northrop
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  2. Claire L. Coleman
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Correspondence to Paul J. Northrop.

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Northrop, P.J., Coleman, C.L. Improved threshold diagnostic plots for extreme value analyses. Extremes 17, 289–303 (2014). https://doi.org/10.1007/s10687-014-0183-z

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Keywords

  • Extreme value theory
  • Generalized Pareto distribution
  • Score test
  • Likelihood ratio test
  • Penultimate approximation
  • Threshold

AMS 2000 Subject Classifications

  • 62G32
  • 62F03
  • 62F05
  • 62P12
  • 62P35