# Statistics of Extremes

@inproceedings{Davison2011StatisticsOE, title={Statistics of Extremes}, author={Anthony C. Davison}, booktitle={International Encyclopedia of Statistical Science}, year={2011} }

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…

## 1,035 Citations

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SummaryMax-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen…

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A censored likelihood procedure is proposed to make inference on these models, together with a threshold selection procedure, goodness-of-fit diagnostics, and a computationally tractable strategy for model selection.

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In Statistics of Extremes, the estimation of parameters of extreme or even rare events is usually done under a semi-parametric framework. The estimators are based on the largest k-ordered statistics…

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- Computer Science
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This paper proposes using the Vecchia approximation, which conveniently decomposes the full joint density into a linear number of low-dimensional conditional density terms based on well-chosen conditioning sets designed to improve and accelerate inference in high dimensions, to fitting complex models with intractable likelihoods.

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