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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 (2004) 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 it suffers from the curse of dimensionality since in a d-dimensional application it involves a d-1-dimensional non-parametric 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 non-trivial. We propose to replace the d-1-dimensional non-parametric 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 mis-specification 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.