Each week, we publish layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format. The Environmetrics Open Access article featured today is available to read here.
Modeling nonstationary extremes of storm severity: Comparing parametric and semiparametric inference
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Current engineering guidelines for the design and assessment of coastal defences and offshore structures require that rare, extreme ocean environments are carefully quantified. Given field measurements or outputs of computer models for the ocean, extreme value analysis can be used to estimate distinctive traits in the tail of distributions of quantities such as significant wave height (quantifying ocean storm severity) and related oceanographic variables. The characteristics of large values of environmental variables such as storm peak significant wave height vary systematically with covariates including storm direction and season in general. Accommodating the effects of non-stationarity is important in practice to ensure that realistic estimates of extreme values are obtained, and that coastal and marine structures are safe in a proportionate manner so as to avoid overcompensation measures.
Two approaches to extreme value analysis are used in the statistics community, referred to as the parametric and semi-parametric approaches. For non-stationary analysis, the parametric approach is more popular in the literature and has had more influential practical uptake; yet the semi-parametric approach has proved useful in overcoming important caveats within the context of extreme values of significant wave height. For analysis of exceedances of a high threshold, the parametric framework assumes a specific (generalised Pareto) functional form for the conditional distribution of exceedances; non-stationarity can be incorporated within the distribution function by allowing the distribution’s parameters to vary with covariates. In the semi-parametric framework, the analysis involves estimation of the extreme value index $\xi$ and related quantities; non-stationarity can be incorporated by performing estimation locally on the covariate domain.
This paper compares non-stationary extreme value analysis using parametric and semi-parametric approaches in a step-by-step manner, highlighting synergies between the approaches in estimating extreme quantiles such as the 𝑇-year level, for quantities such as storm peak significant wave height. A novel heuristic is considered [for estimation of a] non-stationary extreme value threshold with exceedances varying on a circular covariate domain. Hypothesis tests are presented to assess the domain of $\xi$ in the non-stationary setting. Bootstrapping is used to estimate non-stationary confidence bounds for inferred quantities. Practical consequences of the different approaches are explored in application to directional modelling of hindcast storm peak significant wave heights recorded in the North Sea.