The motivation for the work in this thesis is the study of models for extreme values that have clear practical benefit. Specific emphasis is placed on the modelling of extremes of environmental phenomena, which often exhibit spatial or temporal dependence, or both, or are forced by external factors. The peaks-over-threshold approach to modelling extremes combats temporal dependence, providing a way in which likelihood-based methods may he used reliably. The method is widely used and has sound asymptotic foundations. However its performance in practical situations is less well understand. The essence of the method is to identify clusters of extremes and estimate the required extremal properties based only on the cluster peaks. A simulation study is used here to assess the performance of the method. This study shows that while not robust to some of its arbitrary choices, such as cluster identification procedure, if clusters are identified using Ferro and Segers' (2003) automatic procedure then the peaks-over-threshold method typically gives accurate estimates of extremal properties. It is often common for extreme values to be affected by external factors. For example environmental extremes may be expected to behave differently at different times of the year. Incorporating beliefs about external factors was recognised early on in the development of extremal models as an important consideration, and a simple way in which this can be achieved is by allowing parameters of extremal distributions to depend on covariates. The work here considers whether choosing logical covariate forms for variation in parameters leads to improved estimation of extremal properties. It is found that a degree of improved accuracy in estimates can be achieved upon choice of a suitable model. but that the uncertainty in estimates, which is important to report, is poorly quantified.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:555232 |
| Date | January 2011 |
| Creators | Youngman, Ben |
| Publisher | University of Sheffield |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
Page generated in 0.0017 seconds