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postgraduate thesis: Statistical inference of a threshold model in extreme value analysis

TitleStatistical inference of a threshold model in extreme value analysis
Authors
Advisors
Advisor(s):Li, WK
Issue Date2012
PublisherThe University of Hong Kong (Pokfulam, Hong Kong)
Citation
Lee, D. [李大為]. (2012). Statistical inference of a threshold model in extreme value analysis. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4819945
AbstractIn many data sets, a mixture distribution formulation applies when it is known that each observation comes from one of the underlying categories. Even if there are no apparent categories, an implicit categorical structure may justify a mixture distribution. This thesis concerns the modeling of extreme values in such a setting within the peaks-over-threshold (POT) approach. Specifically, the traditional POT modeling using the generalized Pareto distribution is augmented in the sense that, in addition to threshold exceedances, data below the threshold are also modeled by means of the mixture exponential distribution. In the first part of this thesis, the conventional frequentist approach is applied for data modeling. In view of the mixture nature of the problem, the EM algorithm is employed for parameter estimation, where closed-form expressions for the iterates are obtained. A simulation study is conducted to confirm the suitability of such method, and the observation of an increase in standard error due to the variability of the threshold is addressed. The model is applied to two real data sets, and it is demonstrated how computation time can be reduced through a multi-level modeling procedure. With the fitted density, it is possible to derive many useful quantities such as return periods and levels, value-at-risk, expected tail loss and bounds for ruin probabilities. A likelihood ratio test is then used to justify model choice against the simpler model where the thin-tailed distribution is homogeneous exponential. The second part of the thesis deals with a fully Bayesian approach to the same model. It starts with the application of the Bayesian idea to a special case of the model where a closed-form posterior density is computed for the threshold parameter, which serves as an introduction. This is extended to the threshold mixture model by the use of the Metropolis-Hastings algorithm to simulate samples from a posterior distribution known up to a normalizing constant. The concept of depth functions is proposed in multidimensional inference, where a natural ordering does not exist. Such methods are then applied to real data sets. Finally, the issue of model choice is considered through the use of posterior Bayes factor, a criterion that stems from the posterior density.
DegreeMaster of Philosophy
SubjectInference.
Extreme value theory.
Multivariate analysis.
Dept/ProgramStatistics and Actuarial Science

 

DC FieldValueLanguage
dc.contributor.advisorLi, WK-
dc.contributor.authorLee, David.-
dc.contributor.author李大為.-
dc.date.issued2012-
dc.identifier.citationLee, D. [李大為]. (2012). Statistical inference of a threshold model in extreme value analysis. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b4819945-
dc.description.abstractIn many data sets, a mixture distribution formulation applies when it is known that each observation comes from one of the underlying categories. Even if there are no apparent categories, an implicit categorical structure may justify a mixture distribution. This thesis concerns the modeling of extreme values in such a setting within the peaks-over-threshold (POT) approach. Specifically, the traditional POT modeling using the generalized Pareto distribution is augmented in the sense that, in addition to threshold exceedances, data below the threshold are also modeled by means of the mixture exponential distribution. In the first part of this thesis, the conventional frequentist approach is applied for data modeling. In view of the mixture nature of the problem, the EM algorithm is employed for parameter estimation, where closed-form expressions for the iterates are obtained. A simulation study is conducted to confirm the suitability of such method, and the observation of an increase in standard error due to the variability of the threshold is addressed. The model is applied to two real data sets, and it is demonstrated how computation time can be reduced through a multi-level modeling procedure. With the fitted density, it is possible to derive many useful quantities such as return periods and levels, value-at-risk, expected tail loss and bounds for ruin probabilities. A likelihood ratio test is then used to justify model choice against the simpler model where the thin-tailed distribution is homogeneous exponential. The second part of the thesis deals with a fully Bayesian approach to the same model. It starts with the application of the Bayesian idea to a special case of the model where a closed-form posterior density is computed for the threshold parameter, which serves as an introduction. This is extended to the threshold mixture model by the use of the Metropolis-Hastings algorithm to simulate samples from a posterior distribution known up to a normalizing constant. The concept of depth functions is proposed in multidimensional inference, where a natural ordering does not exist. Such methods are then applied to real data sets. Finally, the issue of model choice is considered through the use of posterior Bayes factor, a criterion that stems from the posterior density.-
dc.languageeng-
dc.publisherThe University of Hong Kong (Pokfulam, Hong Kong)-
dc.relation.ispartofHKU Theses Online (HKUTO)-
dc.rightsThe author retains all proprietary rights, (such as patent rights) and the right to use in future works.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.source.urihttp://hub.hku.hk/bib/B4819945X-
dc.subject.lcshInference.-
dc.subject.lcshExtreme value theory.-
dc.subject.lcshMultivariate analysis.-
dc.titleStatistical inference of a threshold model in extreme value analysis-
dc.typePG_Thesis-
dc.identifier.hkulb4819945-
dc.description.thesisnameMaster of Philosophy-
dc.description.thesislevelMaster-
dc.description.thesisdisciplineStatistics and Actuarial Science-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.5353/th_b4819945-
dc.date.hkucongregation2012-

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