Estimation of associated values from conditional extreme value models

Abstract

The design and reanalysis of offshore and coastal structures usually requires the estimation of return values for dominant metocean variables (such as significant wave height) and associated values for other variables (such as peak spectral period or wind speed) from a finite sample of data; these are typically estimated using extreme value analysis. Yet the parameters of extreme value models can only be estimated with error from finite data. Different choices available to summarise uncertain information about the characteristics of the tail of a multivariate distribution in a small number of summary statistics (such as return values and associated values) complicates their estimation, especially for small sample sizes: choices regarding the ordering of mathematical operations lead to estimators of return values and associated values with different finite sample bias and variance characteristics. The current work extends a previous study (Jonathan et al.,2021) into the performance of estimators for marginal return values in the presence of sampling uncertainty, to estimators of associated values based on the bivariate conditional extremes model (Heffernan and Tawn, 2004) and competitors. Using a large designed simulation experiment, we explore the performance of combinations of 12 different estimators and three bivariate model candidates. The rich set of results from the simulation experiment are reported and explained in detail. Briefly: (a) calculation of associated values is only always feasible from small samples using two of the 12 estimators, which should be preferred; (b) estimators exploiting the median rather than the mean to summarise a distribution are more robust, and should also be preferred, especially for small sample sizes; (c) extreme value models incorporating appropriate descriptions of marginal and dependence provide better estimation of associated values for larger sample size; and (d) summarising the joint tail of metocean variables (in terms of return values and associated values) should be avoided where possible, in favour of probabilistic risk analysis of structural failure incorporating full uncertainty propagation.