Statistics of Extremes

  title={Statistics of Extremes},
  author={Anthony C. Davison},
  booktitle={International Encyclopedia of Statistical Science},
  • A. Davison
  • Published in
    International Encyclopedia of…
    17 April 2015
  • Mathematics
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… 
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Non-Stationary Dependence Structures for Spatial Extremes
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High-Order Composite Likelihood Inference for Max-Stable Distributions and Processes
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High-dimensional peaks-over-threshold inference
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Bootstrap and Other Resampling Methodologies in Statistics of Extremes
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Statistics of Extremes: Theory and Applications
Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application
Dependence Measures for Extreme Value Analyses
Quantifying dependence is a central theme in probabilistic and statistical methods for multivariate extreme values. Two situations are possible: one where, in a limiting sense, the extremes are
Space–time modelling of extreme events
Max‐stable processes are the natural analogues of the generalized extreme value distribution when modelling extreme events in space and time. Under suitable conditions, these processes are
Modelling Extreme Multivariate Events
SUMMARY The classical treatment of multivariate extreme values is through componentwise ordering, though in practice most interest is in actual extreme events. Here the point process of observations
Markov chain models for threshold exceedances
In recent research on extreme value statistics, there has been an extensive development of threshold methods, first in the univariate case and subsequently in the multivariate case as well. In this
Likelihood-Based Inference for Max-Stable Processes
The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the
Hierarchical modeling for extreme values observed over space and time
We propose a hierarchical modeling approach for explaining a collection of spatially referenced time series of extreme values. We assume that the observations follow generalized extreme value (GEV)
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We propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence. We