A Review of Extreme Value Threshold Estimation and Uncertainty Quantification

Abstract

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).