Nonparametric smoothing in extreme value theory

• Main Author: Clur, John-Craig
• Other Authors: Haines, Linda
• Format: Dissertation
• Language: English
• Published: University of Cape Town 2014
• Subjects: Financial Mathematics
• Online Access: http://hdl.handle.net/11427/10285

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.