TY - JOUR
T1 - Sparse structures for multivariate extremes
AU - Engelke, Sebastian
AU - Ivanovs, Jevgenijs
N1 - Publisher Copyright:
© 2021 Annual Reviews Inc.. All rights reserved.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/3/7
Y1 - 2021/3/7
N2 - Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well developed, methods for high-dimensional and complex data sets are still scarce. Appropriate notions of sparsity and connections to other fields such as machine learning, graphical models, and high-dimensional statistics have only recently been established. This article reviews the new domain of research concerned with the detection and modeling of sparse patterns in rare events. We first describe the different forms of extremal dependence that can arise between the largest observations of a multivariate random vector. We then discuss the current research topics, including clustering, principal component analysis, and graphical modeling for extremes. Identification of groups of variables that can be concomitantly extreme is also addressed. The methods are illustrated with an application to flood risk assessment.
AB - Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well developed, methods for high-dimensional and complex data sets are still scarce. Appropriate notions of sparsity and connections to other fields such as machine learning, graphical models, and high-dimensional statistics have only recently been established. This article reviews the new domain of research concerned with the detection and modeling of sparse patterns in rare events. We first describe the different forms of extremal dependence that can arise between the largest observations of a multivariate random vector. We then discuss the current research topics, including clustering, principal component analysis, and graphical modeling for extremes. Identification of groups of variables that can be concomitantly extreme is also addressed. The methods are illustrated with an application to flood risk assessment.
KW - conditional independence
KW - dimension reduction
KW - extremal graphical models
KW - extreme value theory
KW - sparsity
UR - http://www.scopus.com/inward/record.url?scp=85095097877&partnerID=8YFLogxK
U2 - 10.1146/annurev-statistics-040620-041554
DO - 10.1146/annurev-statistics-040620-041554
M3 - Review
AN - SCOPUS:85095097877
SN - 2326-8298
VL - 8
SP - 241
EP - 270
JO - Annual Review of Statistics and Its Application
JF - Annual Review of Statistics and Its Application
ER -