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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Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Model-based inference of conditional extreme value distributions with hydrological applications
AU - Towe, Ross Paul
AU - Tawn, Jonathan Angus
AU - Lamb, Robert
AU - Sherlock, Christopher Gerrard
N1 - 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.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - 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.
AB - 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.
U2 - 10.1002/env.2575
DO - 10.1002/env.2575
M3 - Journal article
VL - 30
JO - Environmetrics
JF - Environmetrics
SN - 1180-4009
IS - 8
M1 - e2575
ER -