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    Rights statement: This is the peer reviewed version of the following article: Towe, RP, Tawn, JA, Lamb, R, Sherlock, C. Model‐based inference of conditional extreme value distributions with hydrological applications. Environmetrics. 2019. doi: 10.1002/env.2575 which has been published in final form at https://onlinelibrary.wiley.com/doi/full/10.1002/env.2575 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.

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    Embargo ends: 29/04/20

    Available under license: CC BY: Creative Commons Attribution 4.0 International License

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Model-based inference of conditional extreme value distributions with hydrological applications

Research output: Contribution to journalJournal article

E-pub ahead of print
Article numbere2575
<mark>Journal publication date</mark>29/04/2019
<mark>Journal</mark>Environmetrics
Number of pages20
Publication statusE-pub ahead of print
Early online date29/04/19
Original languageEnglish

Abstract

Multivariate extreme value models are used to estimate joint risk in a number of applications, with a particular focus on environmental fields ranging from climatology and hydrology to oceanography and seismic hazards. The semi-parametric conditional extreme value model of Heffernan and Tawn involving a multivariate regression provides the most suitable of current statistical models in terms of its flexibility to handle a range of extremal dependence classes. However, the standard inference for the joint distribution of the residuals of this model suffers from the curse of dimensionality because, in a d-dimensional application, it involves a d−1-dimensional nonparametric density estimator, which requires, for accuracy, a number points and commensurate effort that is exponential in d. Furthermore, it does not allow for any partially missing observations to be included, and a previous proposal to address this is extremely computationally intensive, making its use prohibitive if the proportion of missing data is nontrivial. We propose to replace the d−1-dimensional nonparametric density estimator with a model-based copula with univariate marginal densities estimated using kernel methods. This approach provides statistically and computationally efficient estimates whatever the dimension, d, or the degree of missing data. Evidence is presented to show that the benefits of this approach substantially outweigh potential misspecification errors. The methods are illustrated through the analysis of UK river flow data at a network of 46 sites and assessing the rarity of the 2015 floods in North West England.

Bibliographic note

This is the peer reviewed version of the following article: Towe, RP, Tawn, JA, Lamb, R, Sherlock, C. Model‐based inference of conditional extreme value distributions with hydrological applications. Environmetrics. 2019. doi: 10.1002/env.2575 which has been published in final form at https://onlinelibrary.wiley.com/doi/full/10.1002/env.2575 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.