🤖 AI Summary
Threshold selection critically influences inference in extreme value analysis, yet its associated uncertainty is often overlooked. This study presents the first systematic evaluation of over forty threshold selection methods, integrating Hill estimators, visual diagnostics, goodness-of-fit tests, and extended generalized Pareto models. Through comprehensive simulation experiments and empirical analysis of the Padua daily rainfall series, the work assesses the statistical performance and applicability conditions of each method. The authors propose an automated strategy for optimal threshold selection and identify several approaches that exhibit superior robustness and efficiency. These findings offer practical guidance for improving reliability in extreme value modeling.
📝 Abstract
One of the two dominant approaches for univariate extreme value analysis is to model exceedances above a large threshold, the choice of which has a large impact on inference and whose uncertainty is often subsequently ignored. In this article we review more than 40 threshold selection procedures, including semiparametric methods based on Hill's estimator, visual diagnostics, goodness-of-fit tests, and others based on extended generalized Pareto models. Starting with the statistical properties underlying the various proposals, we provide a critical assessment of their strengths and weaknesses, discuss how they might be automated and describe the results of an extensive simulation study used to identify the most promising procedures. The approaches are compared using a long time series of daily rainfall totals from Padova.