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 -