Likelihood‐based procedures for threshold diagnostics and uncertainty in extreme value modelling

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Automated threshold selection for extreme value analysis via ordered goodness-of-fit tests with adjustment for false discovery rate (2018, background): “Methods in the third category are based on mixtures of a GPD for the tail and another distribution for the “bulk” joined at the threshold [e.g., MacDonald et al. (2011), Wadsworth and Tawn (2012), Naveau et al. (2016)].”
Extended generalised Pareto models for tail estimation (2011, methodology): “Wadsworth and Tawn (2011) exploit penultimate theory to model threshold uncertainty and provide a likelihood ratio testing procedure for the threshold selection.”
Cross‐validatory extreme value threshold selection and uncertainty with application to ocean storm severity (2015, methodology): “Given the slow convergence in this case it may be that much higher thresholds should be explored, requiring much larger simulated sample sizes, such as those used by Wadsworth and Tawn (2012).”
Improved threshold diagnostic plots for extreme value analyses (2014, methodology): “1.2 A piecewise constant shape parameter approximation Wadsworth and Tawn (2012) propose a penultimate NHPP model in which the shape parameter is modelled as a piecewise constant function of threshold.”