Includes bibliographical references (leaves 137-138). / This work investigates the modelling of non-stationary sample extremes using a roughness penalty approach, in which smoothed natural cubic splines are fitted to the location and scale parameters of the generalized extreme value distribution and the distribution of the r largest order statistics. Estimation is performed by implementing a Fisher scoring algorithm to maximize the penalized log-likelihood function. The approach provides a flexible framework for exploring smooth trends in sample extremes, with the benefit of balancing the trade-off between 'smoothness' and adherence to the underlying data by simply changing the smoothing parameter. To evaluate the overall performance of the extreme value theory methodology in smoothing extremes a simulation study was performed.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uct/oai:localhost:11427/10285 |
| Date | January 2010 |
| Creators | Clur, John-Craig |
| Contributors | Haines, Linda |
| Publisher | University of Cape Town, Faculty of Science, Department of Statistical Sciences |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Master Thesis, Masters, MSc |
| Format | application/pdf |
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