Multivariate Extreme Value Theory - A Tutorial with Applications to Hydrology and Meteorology

Anne Dutfoy,Nicolas Roche,Sylvie Parey

doi:10.2478/demo-2014-0003

Anne Dutfoy, Nicolas Roche + Show 1 more

Open Access

https://doi.org/10.2478/demo-2014-0003

Copy DOI

Journal: Dependence Modeling	Publication Date: Jan 2, 2014
Citations: 17	License type: cc-by

Affiliation: Électricité de France (France)

Abstract

AbstractIn this paper, we provide a tutorial on multivariate extreme value methods which allows to estimate the risk associated with rare events occurring jointly. We draw particular attention to issues related to extremal dependence and we insist on the asymptotic independence feature. We apply the multivariate extreme value theory on two data sets related to hydrology and meteorology: first, the joint flooding of two rivers, which puts at risk the facilities lying downstream the confluence; then the joint occurrence of high speed wind and low air temperatures, which might affect overhead lines.

Highlights

In many elds, we are interested in modeling extreme hazards in order to estimate the risk that a particular community or industrial structure incurs
The univariate extreme value theory is relatively standard to model the tail of the distribution of a scalar random variable: it provides an asymptotic justi cation for the generalized Pareto distribution to be an appropriate model for the distributoin of excesses over a suitably chosen high threshold ([1, 10])
We showed that multivariate extreme value distributions only allow to model asymptotic independence through p = O( /z )

Summary

Introduction

We are interested in modeling extreme hazards in order to estimate the risk that a particular community or industrial structure incurs. This section is devoted to the main results of the multivariate extreme value theory and presents some methods for multivariate inference It explains the speci cities of the multivariate framework compared to the univariate one. The component-wise maximum of observations might not correspond to one observed data, which makes any approach based on the component-wise maximum delicate to handle In relation with the latter issue, the de nition of what makes a multivariate observation extreme is rather tricky: is it enough that just a single coordinate attains an exceptional value, or should it be extreme in all dimensions simultaneously?. A fundamentally new issue arising in the multivariate context is that of dependence, which describes how margninal extremes interact

Key results

Summary and Conclusion