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

TL;DR

This paper introduces a model-based copula approach for efficient inference of multivariate extreme value distributions, improving handling of high-dimensional data and missing observations in environmental applications.

Contribution

It replaces the non-parametric density estimator in the Heffernan and Tawn model with a copula, enabling scalable and efficient inference in high dimensions and with missing data.

Findings

Efficient estimation of multivariate extremes in high dimensions.

Successful application to UK river flow data and flood risk assessment.

Outperforms traditional methods in computational speed and flexibility.

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 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.