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Automated threshold selection methods for extreme wave analysis
Coastal Engineering, Volume: 56, Issue: 10, Pages: 1013 - 1021
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The study of the extreme values of a variable such as wave height is very important in flood risk assessmentand coastal design. Often values above a sufficiently large threshold can be modelled using the GeneralizedPareto Distribution, the parameters of which are estimated using maximum likelihood....
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The study of the extreme values of a variable such as wave height is very important in flood risk assessmentand coastal design. Often values above a sufficiently large threshold can be modelled using the GeneralizedPareto Distribution, the parameters of which are estimated using maximum likelihood. There are severalpopular empirical techniques for choosing a suitable threshold, but these require the subjectiveinterpretation of plots by the user.We in this paper present a pragmatic automated, simple and computationally inexpensive threshold selectionmethod based on the distribution of the difference of parameter estimates when the threshold is changed,and apply it to a published rainfall and a new wave height data set. We assess the effect of the uncertaintyassociated with our threshold selection technique on return level estimation by using the bootstrapprocedure. We illustrate the effectiveness of our methodology by a simulation study and compare it with theapproach used in the JOINSEA software. In addition, we present an extension that allows the thresholdselected to depend on the value of a covariate such as the cosine of wave direction.
Bootstrap, Covariate dependent thresholds, Distribution with Generalized Pareto tail, Generalized Pareto Distribution, GPD,Return level confidence intervals
School of Management