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Use of extreme value theory for making statistical inference about endpoints of distributions, with applications in global optimization and meteorology

Hamilton, Emily Alexandra 2008. Use of extreme value theory for making statistical inference about endpoints of distributions, with applications in global optimization and meteorology. PhD Thesis, Cardiff University.

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Abstract

We use extreme value theory to make statistical inference about the endpoint of distributions. First we compare estimators of the endpoint of several distributions, including a distribution that appears in problems of global optimization. These estimators use a fixed number of order statistics (k) from a sample of fixed size (n). Two of the estimators investigated are the optimal linear estimator and the maximum likelihood estimator. We find that the optimal linear estimator often outperforms the maximum likelihood estimator. We next investigate how the order statistics change as sample size increases. In order to do this, we define record times: the sample size at which the set of k smallest order statistics changes. We give the distributions of several statistics related to order statistics and record times, in particular we show that records occur according to a nonhomogeneous Poisson process. We show that order statistics can be modeled using a Markov chain, and use this Markov chain to investigate estimators of the endpoint of a distribution. Two additional estimators are derived and investigated using the Markov chain model. Finally, we consider a meteorological application of extreme value theory. In particular, we estimate the maximum and minimum sea level at several ports in the Netherlands. This is done using a combination of record theory, singular spectrum decomposition and known estimators of the endpoint of a distribution.

Item Type: Thesis (PhD)
Status: Unpublished
Schools: Mathematics
Subjects: Q Science > QA Mathematics
ISBN: 9781303214035
Funders: EPSRC
Date of First Compliant Deposit: 30 March 2016
Last Modified: 12 Feb 2016 23:13
URI: http://orca-mwe.cf.ac.uk/id/eprint/54789

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