Nonparametric smoothing in extreme value theory
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 a...
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| Format: | Dissertation |
| Language: | English |
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University of Cape Town
2014
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| Online Access: | http://hdl.handle.net/11427/10285 |
| Summary: | 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. |
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