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Gomes, M. Ivette; Guillou, Armelle

Extreme value theory and statistics of univariate extremes: a review. (English) Zbl 07763438

Int. Stat. Rev. 83, No. 2, 263-292 (2015).
Summary: Statistical issues arising in modelling univariate extremes of a random sample have been successfully used in the most diverse fields, such as biometrics, finance, insurance and risk theory. Statistics of univariate extremes (SUE), the subject to be dealt with in this review paper, has recently faced a huge development, partially because rare events can have catastrophic consequences for human activities, through their impact on the natural and constructed environments. In the last decades, there has been a shift from the area of parametric SUE, based on probabilistic asymptotic results in extreme value theory, towards semi-parametric approaches. After a brief reference to Gumbel’s block methodology and more recent improvements in the parametric framework, we present an overview of the developments on the estimation of parameters of extreme events and on the testing of extreme value conditions under a semi-parametric framework. We further discuss a few challenging topics in the area of SUE.
© 2014 The Authors. International Statistical Review © 2014 International Statistical Institute
{©2014 The Authors. International Statistical Review © 2014 International Statistical Institute}

Cited in 35 Documents

MSC:

62-XX Statistics

Keywords:

statistics of univariate extremes; parametric and semi-parametric approaches; extreme value index and tail parameters; testing issues

Software:

ismev; AS 215
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References:

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