University of Newcastle upon Tyne

School of Mathematics and Statistics

Statistics Seminars 2005-2006

2 December 2005, L401, 2:15pm

Professor Jonathan Tawn, Lancaster University

Abstract

Statistical methods for the application of multivariate extreme value theory have developed rapidly over the last 20 years. A wide range of methods, including parametric and nonparametric approaches, have been proposed.

Despite this development almost all published applications are bivariate, with one or two notable exceptions, and they tend not to address the practical data handling issues that arise with real applications. In this talk I will outline two major environmental studies where multivariate extreme value methods are being applied.

First I will introduce the multivariate extreme value method that I will use as a starting point in each application, this is the conditional approach of Heffernan and Tawn (2004, JRSS B).

In the first study the spatial extremes of sea surges in the North Sea are modelled. We have numerical model hindcast hourly surge data on a grid of
259 sites for the period of 1955-2000. The numerical model was driven by a high-quality hindcast of the meteorology for this period and had been shown to reproduce the surge well at observational sites. The talk will focus on estimating the characteristics of the spatial field of extreme values; this is important for the insurance industry for determining offshore and coastal loss distributions. The large dimension of the problem leads to new problems related to the visualisation of the fitted dependence structure, parsimony, identifying the minimum number of sites to capture most dependence, and the generation of super-storms.

In the second study we have assess to daily river flow data at the entire UK network of sites. We are interested in estimating the risk of flooding over different gauges along a river and for gauges in different rivers given that flooding is observed at a given gauge. The feature we will emphasise is the large amount of missing data over the entire network. Currently no methods exist for handling missing data in multivariate extreme values, consequently the default is to analyse only those data observed simultaneously on all variables. Such an approach is potentially highly inefficient relative to having access to the full data. In the talk we will introduce an approach for handling the missing data in multivariate extremes and illustrate its efficiency properties.

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