Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures

Handle URI:
http://hdl.handle.net/10754/625177
Title:
Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures
Authors:
Huser, Raphaël ( 0000-0002-1228-2071 ) ; Opitz, Thomas; Thibaud, Emeric
Abstract:
Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Huser R, Opitz T, Thibaud E (2017) Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures. Spatial Statistics. Available: http://dx.doi.org/10.1016/j.spasta.2017.06.004.
Publisher:
Elsevier BV
Journal:
Spatial Statistics
Issue Date:
23-Jun-2017
DOI:
10.1016/j.spasta.2017.06.004
Type:
Article
ISSN:
2211-6753
Sponsors:
We thank Amanda Hering (Baylor University) for sharing the wind data and Luigi Lombardo (KAUST) for cartographic support. This work was undertaken while Emeric Thibaud was at Colorado State University with partial support by US National Science Foundation Grant DMS-1243102. Thomas Opitz was partially supported by the French national programme LEFE/INSU .
Additional Links:
http://www.sciencedirect.com/science/article/pii/S221167531730088X
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorHuser, Raphaëlen
dc.contributor.authorOpitz, Thomasen
dc.contributor.authorThibaud, Emericen
dc.date.accessioned2017-07-12T07:20:54Z-
dc.date.available2017-07-12T07:20:54Z-
dc.date.issued2017-06-23en
dc.identifier.citationHuser R, Opitz T, Thibaud E (2017) Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures. Spatial Statistics. Available: http://dx.doi.org/10.1016/j.spasta.2017.06.004.en
dc.identifier.issn2211-6753en
dc.identifier.doi10.1016/j.spasta.2017.06.004en
dc.identifier.urihttp://hdl.handle.net/10754/625177-
dc.description.abstractGaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.en
dc.description.sponsorshipWe thank Amanda Hering (Baylor University) for sharing the wind data and Luigi Lombardo (KAUST) for cartographic support. This work was undertaken while Emeric Thibaud was at Colorado State University with partial support by US National Science Foundation Grant DMS-1243102. Thomas Opitz was partially supported by the French national programme LEFE/INSU .en
dc.publisherElsevier BVen
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S221167531730088Xen
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Spatial Statistics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Spatial Statistics, [, , (2017-06-23)] DOI: 10.1016/j.spasta.2017.06.004 . © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectAsymptotic dependence and independenceen
dc.subjectCensored likelihood inferenceen
dc.subjectSpatial copulaen
dc.subjectExtreme eventen
dc.subjectRandom scale modelen
dc.subjectThreshold exceedanceen
dc.titleBridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixturesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalSpatial Statisticsen
dc.eprint.versionPost-printen
dc.contributor.institutionINRA, UR546 Biostatistics and Spatial Processes, 228, Route de l’Aérodrome, CS 40509, 84914 Avignon, Franceen
dc.contributor.institutionPolytechnique Fédérale de Lausanne, EPFL SB MATH STAT, Station 8, 1015 Lausanne, Switzerlanden
kaust.authorHuser, Raphaëlen
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