Statistics of Extremes

Handle URI:
http://hdl.handle.net/10754/564140
Title:
Statistics of Extremes
Authors:
Davison, Anthony C.; Huser, Raphaël ( 0000-0002-1228-2071 )
Abstract:
Statistics of extremes concerns inference for rare events. Often the events have never yet been observed, and their probabilities must therefore be estimated by extrapolation of tail models fitted to available data. Because data concerning the event of interest may be very limited, efficient methods of inference play an important role. This article reviews this domain, emphasizing current research topics. We first sketch the classical theory of extremes for maxima and threshold exceedances of stationary series. We then review multivariate theory, distinguishing asymptotic independence and dependence models, followed by a description of models for spatial and spatiotemporal extreme events. Finally, we discuss inference and describe two applications. Animations illustrate some of the main ideas. © 2015 by Annual Reviews. All rights reserved.
KAUST Department:
Applied Mathematics and Computational Science Program
Publisher:
Annual Reviews
Journal:
Annual Review of Statistics and Its Application
Issue Date:
10-Apr-2015
DOI:
10.1146/annurev-statistics-010814-020133
Type:
Article
ISSN:
23268298
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorDavison, Anthony C.en
dc.contributor.authorHuser, Raphaëlen
dc.date.accessioned2015-08-03T12:33:50Zen
dc.date.available2015-08-03T12:33:50Zen
dc.date.issued2015-04-10en
dc.identifier.issn23268298en
dc.identifier.doi10.1146/annurev-statistics-010814-020133en
dc.identifier.urihttp://hdl.handle.net/10754/564140en
dc.description.abstractStatistics of extremes concerns inference for rare events. Often the events have never yet been observed, and their probabilities must therefore be estimated by extrapolation of tail models fitted to available data. Because data concerning the event of interest may be very limited, efficient methods of inference play an important role. This article reviews this domain, emphasizing current research topics. We first sketch the classical theory of extremes for maxima and threshold exceedances of stationary series. We then review multivariate theory, distinguishing asymptotic independence and dependence models, followed by a description of models for spatial and spatiotemporal extreme events. Finally, we discuss inference and describe two applications. Animations illustrate some of the main ideas. © 2015 by Annual Reviews. All rights reserved.en
dc.publisherAnnual Reviewsen
dc.subjectAsymptotic dependenceen
dc.subjectAsymptotic independenceen
dc.subjectExtrapolationen
dc.subjectGeneralized extreme value distributionen
dc.subjectGeneralized Pareto distributionen
dc.subjectMax-stabilityen
dc.subjectPareto processen
dc.subjectPeaks over thresholdsen
dc.subjectPoisson processen
dc.titleStatistics of Extremesen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalAnnual Review of Statistics and Its Applicationen
dc.contributor.institutionEcole Polytechnique Fédérale de LausanneLausanne, Switzerlanden
kaust.authorHuser, Raphaëlen
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