ABSTRACT

Extreme value theory provides a relatively robust, asymptotically motivated, basis for drawing statistical inferences about the magnitude & frequency of events which are extreme and rare. Extreme value methods are widely used in discplines such as hydrology, finance and engineering to quantify the risks associated with catastrophic events such as the breach of a sea wall, the failure of a component within a machine, or a collapse in the value of a portfolio of investments.

Primary interest often lies in describing changes in the magnitude and frequency with which extreme events occur, and we review parametric and nonparametric approaches to the detection and quantification of trends in the characteristics of extreme events. We illustrate the different approaches by analysing changes in the characteristics of North Sea storm surges during the second half of the 20th century, a substantive application which requires us to adapt and extend the existing statistical methodology.