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Improved threshold diagnostic plots for extreme value analyses

Content Provider	Springer Nature Link
Author	rthrop, Paul J. Coleman, Claire L.
Copyright Year	2014
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.
Starting Page	289
Ending Page	303
Page Count	15
File Format	PDF
ISSN	13861999
Journal	Extremes
Volume Number	17
Issue Number	2
e-ISSN	1572915X
Language	English
Publisher	Springer US
Publisher Date	2014-03-07
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Extreme value theory Generalized Pareto distribution Score test Likelihood ratio test Penultimate approximation Threshold Statistics Quality Control, Reliability, Safety and Risk Civil Engineering Hydrogeology Environmental Management Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Economics, Econometrics and Finance Engineering

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