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Modelling spatially-dependent non-stationary extremes with application to hurricane-induced wave heights

Northrop, PJ; Jonathan, P; (2010) Modelling spatially-dependent non-stationary extremes with application to hurricane-induced wave heights. Department of Statistical Science, University College London

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Abstract

In environmental applications it is found frequently that the extremes of a variable of interest are non-stationary, varying systematically in space, time or with the values of covariates. Multi-site datasets are common, and in such cases there is likely to be non-negligible inter-site dependence. We consider applications in which multi-site data are used to infer the marginal behaviour of the extremes at individual sites, while making proper adjustment for inter-site dependence. For reasons of statistical e ciency, modern extreme value analyses often model exceedances of a high threshold. Choosing an appro- priate threshold can be problematic, particularly if the extremes are non-stationary. We propose a method for setting covariate-dependent threshold using quantile regression. We consider how the quantile regression model and extreme value models tted to threshold exceedances should be parameterised, in order that they are compatible. These consid- erations also suggest a new technique for selecting the level of extreme value thresholds. We adjust estimates of uncertainty for spatial dependence using methodology proposed recently. These methods are illustrated using time series of storm peak signi cant wave heights from 72 sites in the Gulf of Mexico.

Type:Report
Title:Modelling spatially-dependent non-stationary extremes with application to hurricane-induced wave heights
Publisher version:http://www.ucl.ac.uk/Stats/research/reports/psfiles/rr306.pdf
Keywords:Extreme value regression modelling, dependent data, quantile regression, threshold exceedances, threshold selection, wave heights
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science

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