A review of extreme value threshold estimation and uncertainty quantification. (English) Zbl 1297.62120

Summary: The last decade has seen development of a plethora of approaches for threshold estimation in extreme value applications. From a statistical perspective, the threshold is loosely defined such that the population tail can be well approximated by an extreme value model (e.g., the generalised Pareto distribution), obtaining a balance between the bias due to the asymptotic tail approximation and parameter estimation uncertainty due to the inherent sparsity of threshold excess data. This paper reviews recent advances and some traditional approaches, focusing on those that provide quantification of the associated uncertainty on inferences (e.g., return level estimation).


62G32 Statistics of extreme values; tail inference
62G07 Density estimation
62G30 Order statistics; empirical distribution functions
62E20 Asymptotic distribution theory in statistics
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