Statistics of Extremes

Anthony C. Davison, Raphaël Huser

Research output: Contribution to journalArticlepeer-review

62 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)203-235
Number of pages33
JournalAnnual Review of Statistics and Its Application
Volume2
Issue number1
DOIs
StatePublished - Apr 10 2015

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