Modeling nonstationary extremes of storm severity:Comparing parametric and semiparametric inference

This article compares the modeling of nonstationary extreme events using parametric models with local parametric and semiparametric approaches also motivated by extreme value theory. Specifically, three estimators are compared based on (a) (local) semiparametric moment estimation, (b) (local) maximum likelihood estimation, and (c) spline-based maximum likelihood estimation. Inference is performed in a sequential manner, highlighting the synergies between the different approaches to estimating extreme quantiles, including the T-year level and right endpoint when finite. We present a novel heuristic to estimate nonstationary extreme value threshold with exceedances varying on a circular domain, and hypothesis-testing procedures for identifying max-domain of attraction in the nonstationary setting. Bootstrapping is used to estimate nonstationary confidence bounds throughout. We provide step-by-step guides for estimation, and explore the different inference strategies in application to directional modeling of hindcast storm peak significant wave heights recorded in the North Sea. © 2021 The Authors. Environmetrics published by John Wiley & Sons, Ltd