Practical non-stationary extreme value analysis of peaks over threshold using the generalised Pareto distribution : Estimating uncertainties in return values

Tendijck, Stan and Randell, David and Feld, Graham and Jonathan, Philip (2024) Practical non-stationary extreme value analysis of peaks over threshold using the generalised Pareto distribution : Estimating uncertainties in return values. Ocean Engineering, 312: 119247. ISSN 0029-8018

Abstract

Choice of tuning parameters influences the performance of non-stationary extreme value modelling for peaks over threshold using the generalised Pareto (GP) distribution. We examine the effect of tuning parameter choice on maximum roughness-penalised likelihood estimation of GP models, the shape and scale parameters of which are assumed to vary smoothly on a one-dimensional “directional” covariate domain, under a B-spline representation. We examine the effect of (a) extreme value model parameterisation, (b) relative roughness penalty of GP parameters as a function of covariate, (c) cross-validation strategy for roughness parameter tuning, and (d) estimator for return value, on the estimation of return values corresponding to return periods 1000 × the period of a sample of size 1000. Bootstrap resampling is used for thorough uncertainty quantification. We also compare results with those from stationary inference. Results from a large simulation study of 16 cases broadly representative of North Sea conditions for significant wave height with direction, indicate that (i) multiple two-group cross-validation yields lower return value estimates that ten-group cross-validation (leading to negative bias on average, for the case studies considered), (ii) the quantile of the bootstrap predictive estimator yields larger values than the mean over bootstraps of the quantile estimate (leading to reduced omni-directional bias for the case studies considered). Further, (iii) the use of stationary models for non-stationary tails is only reasonable when a high extreme value threshold is set for the stationary analysis. However, (iv) the relative performance of different modelling strategies is sensitive to the specific characteristics of the case study.