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Sparse structures for multivariate extremes

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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.

Original languageEnglish
JournalAnnual Review of Statistics and Its Application
Pages (from-to)241-270
Number of pages30
Publication statusPublished - 7 Mar 2021

Bibliographical note

Publisher Copyright:
© 2021 Annual Reviews Inc.. All rights reserved.

Copyright 2021 Elsevier B.V., All rights reserved.

    Research areas

  • conditional independence, dimension reduction, extremal graphical models, extreme value theory, sparsity

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