A comparison of dependence function estimators in multivariate extremes

Handle URI:
http://hdl.handle.net/10754/623662
Title:
A comparison of dependence function estimators in multivariate extremes
Authors:
Vettori, Sabrina ( 0000-0003-3442-5405 ) ; Huser, Raphaël ( 0000-0002-1228-2071 ) ; Genton, Marc G. ( 0000-0001-6467-2998 )
Abstract:
Various nonparametric and parametric estimators of extremal dependence have been proposed in the literature. Nonparametric methods commonly suffer from the curse of dimensionality and have been mostly implemented in extreme-value studies up to three dimensions, whereas parametric models can tackle higher-dimensional settings. In this paper, we assess, through a vast and systematic simulation study, the performance of classical and recently proposed estimators in multivariate settings. In particular, we first investigate the performance of nonparametric methods and then compare them with classical parametric approaches under symmetric and asymmetric dependence structures within the commonly used logistic family. We also explore two different ways to make nonparametric estimators satisfy the necessary dependence function shape constraints, finding a general improvement in estimator performance either (i) by substituting the estimator with its greatest convex minorant, developing a computational tool to implement this method for dimensions $$D\ge 2$$D≥2 or (ii) by projecting the estimator onto a subspace of dependence functions satisfying such constraints and taking advantage of Bernstein–Bézier polynomials. Implementing the convex minorant method leads to better estimator performance as the dimensionality increases.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Vettori S, Huser R, Genton MG (2017) A comparison of dependence function estimators in multivariate extremes. Statistics and Computing. Available: http://dx.doi.org/10.1007/s11222-017-9745-7.
Publisher:
Springer Nature
Journal:
Statistics and Computing
Issue Date:
11-May-2017
DOI:
10.1007/s11222-017-9745-7
Type:
Article
ISSN:
0960-3174; 1573-1375
Additional Links:
http://link.springer.com/article/10.1007/s11222-017-9745-7; https://stsda.kaust.edu.sa/Documents/2017.VHG.SC.final.pdf
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorVettori, Sabrinaen
dc.contributor.authorHuser, Raphaëlen
dc.contributor.authorGenton, Marc G.en
dc.date.accessioned2017-05-18T08:39:57Z-
dc.date.available2017-05-18T08:39:57Z-
dc.date.issued2017-05-11en
dc.identifier.citationVettori S, Huser R, Genton MG (2017) A comparison of dependence function estimators in multivariate extremes. Statistics and Computing. Available: http://dx.doi.org/10.1007/s11222-017-9745-7.en
dc.identifier.issn0960-3174en
dc.identifier.issn1573-1375en
dc.identifier.doi10.1007/s11222-017-9745-7en
dc.identifier.urihttp://hdl.handle.net/10754/623662-
dc.description.abstractVarious nonparametric and parametric estimators of extremal dependence have been proposed in the literature. Nonparametric methods commonly suffer from the curse of dimensionality and have been mostly implemented in extreme-value studies up to three dimensions, whereas parametric models can tackle higher-dimensional settings. In this paper, we assess, through a vast and systematic simulation study, the performance of classical and recently proposed estimators in multivariate settings. In particular, we first investigate the performance of nonparametric methods and then compare them with classical parametric approaches under symmetric and asymmetric dependence structures within the commonly used logistic family. We also explore two different ways to make nonparametric estimators satisfy the necessary dependence function shape constraints, finding a general improvement in estimator performance either (i) by substituting the estimator with its greatest convex minorant, developing a computational tool to implement this method for dimensions $$D\ge 2$$D≥2 or (ii) by projecting the estimator onto a subspace of dependence functions satisfying such constraints and taking advantage of Bernstein–Bézier polynomials. Implementing the convex minorant method leads to better estimator performance as the dimensionality increases.en
dc.publisherSpringer Natureen
dc.relation.urlhttp://link.springer.com/article/10.1007/s11222-017-9745-7en
dc.relation.urlhttps://stsda.kaust.edu.sa/Documents/2017.VHG.SC.final.pdfen
dc.rightsThe final publication is available at Springer via http://dx.doi.org/10.1007/s11222-017-9745-7en
dc.subjectAsymmetric logistic modelen
dc.subjectComponentwise maximaen
dc.subjectConvexityen
dc.subjectCopulaen
dc.subjectGreatest convex minoranten
dc.subjectNonparametric and parametric estimatorsen
dc.subjectPickands dependence functionen
dc.titleA comparison of dependence function estimators in multivariate extremesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalStatistics and Computingen
dc.eprint.versionPost-printen
kaust.authorVettori, Sabrinaen
kaust.authorHuser, Raphaëlen
kaust.authorGenton, Marc G.en
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