Statistics of Extremes

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Annual Review of Statistics and Its Application, ISSN: 2326-831X, Vol: 2, Issue: 1, Page: 203-235

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Davison, Anthony C.; Huser, Raphael Georges
Annual Reviews
Mathematics; Decision Sciences; Asymptotic dependence; Asymptotic independence; Extrapolation; Generalized extreme value distribution; Generalized Pareto distribution; Max-stability; Pareto process; Peaks over thresholds; Poisson process
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article description
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.