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PORT Hill and Moment Estimators for Heavy-Tailed Models

2008Journal article Restricted access
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dc.contributor.authorGomes, M. Ivette
dc.contributor.authorAlves, M. Isabel Fraga
dc.contributor.authorSantos, Paulo Araújo
dc.date.accessioned2020-07-16T10:32:55Z
dc.date.available2020-07-16T10:32:55Z
dc.date.issued2008
dc.description.abstractIn this article, we use the peaks over random threshold (PORT)-methodology, and consider Hill and moment PORT-classes of extreme value index estimators. These classes of estimators are invariant not only to changes in scale, like the classical Hill and moment estimators, but also to changes in location. They are based on the sample of excesses over a random threshold, the order statistic X[np]+1:n, 0 ≤ p < 1, being p a tuning parameter, which makes them highly flexible. Under convenient restrictions on the underlying model, these classes of estimators are consistent and asymptotically normal for adequate values of k, the number of top order statistics used in the semi-parametric estimation of the extreme value index γ. In practice, there may however appear a stability around a value distant from the target γ when the minimum is chosen for the random threshold, and attention is drawn for the danger of transforming the original data through the subtraction of the minimum. A new bias-corrected moment estimator is also introduced. The exact performance of the new extreme value index PORT-estimators is compared, through a large-scale Monte-Carlo simulation study, with the original Hill and moment estimators, the bias-corrected moment estimator, and one of the minimum-variance reduced-bias (MVRB) extreme value index estimators recently introduced in the literature. As an empirical example we estimate the tail index associated to a set of real data from the field of finance.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationGomes, M. I., Alves, M. I., & Santos, P. (2008). PORT Hill and moment estimators for Heavy-Tailed Models. Communications in Statistics : Simulation & Computation, 37(7), 1281–1306. doi: 10.1080/03610910802050910pt_PT
dc.identifier.doi10.1080/03610910802050910pt_PT
dc.identifier.issn0361-0918
dc.identifier.issn1532-4141
dc.identifier.urihttp://hdl.handle.net/10400.15/2992
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherTaylor & Francispt_PT
dc.relation.publisherversionhttps://www.tandfonline.com/doi/abs/10.1080/03610910802050910pt_PT
dc.subjectExtreme value indexpt_PT
dc.subjectMonte Carlo simulationpt_PT
dc.subjectReduced-bias estimationpt_PT
dc.subjectSample of excessespt_PT
dc.subjectSemi-parametric estimationpt_PT
dc.subjectStatistics of extremespt_PT
dc.subjectStatistics of extremespt_PT
dc.titlePORT Hill and Moment Estimators for Heavy-Tailed Modelspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage1306pt_PT
oaire.citation.issue7pt_PT
oaire.citation.startPage1281pt_PT
oaire.citation.titleCommunications in Statistics - Simulation and Computationpt_PT
oaire.citation.volume37pt_PT
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT

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