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Extreme Value Theory and Statistics of Univariate Extremes: A Review
Author(s) -
Gomes M. Ivette,
Guillou Armelle
Publication year - 2015
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12058
Subject(s) - univariate , extreme value theory , gumbel distribution , parametric statistics , probabilistic logic , nonparametric statistics , econometrics , statistics , parametric model , computer science , actuarial science , mathematics , economics , multivariate statistics
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