Clustering of high values in random fields

Pereira, L.; Martins, Ana Paula; Ferreira, Helena

Publication

Clustering of high values in random fields

2017Journal article

dc.contributor.author	Pereira, L.
dc.contributor.author	Martins, Ana Paula
dc.contributor.author	Ferreira, Helena
dc.date.accessioned	2020-01-09T14:42:08Z
dc.date.available	2020-01-09T14:42:08Z
dc.date.issued	2017
dc.description.abstract	The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with Z2, and that they satisfy stationarity and isotropy conditions. Here we extend the existing theory, concerning the asymptotic behavior of the maximum and the extremal index, to non-stationary and anisotropic random fields, defined over discrete subsets of R2.We show that, under a suitable coordinatewise mixing condition, the maximum may be regarded as the maximum of an approximately independent sequence of submaxima, although there may be high local dependence leading to clustering of high values. Under restrictions on the local path behavior of high values, criteria are given for the existence and value of the spatial extremal index which plays a key role in determining the cluster sizes and quantifying the strength of dependence between exceedances of high levels. The general theory is applied to the class of max-stable random fields, for which the extremal index is obtained as a function of well-known tail dependence measures found in the literature, leading to a simple estimation method for this parameter. The results are illustrated with non-stationary Gaussian and 1-dependent random fields. For the latter, a simulation and estimation study is performed.	pt_PT
dc.description.version	info:eu-repo/semantics/publishedVersion	pt_PT
dc.identifier.doi	10.1007/s10687-017-0291-7	pt_PT
dc.identifier.uri	http://hdl.handle.net/10400.6/8165
dc.language.iso	eng	pt_PT
dc.peerreviewed	yes	pt_PT
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/	pt_PT
dc.subject	Random field	pt_PT
dc.subject	Max-stable process	pt_PT
dc.subject	Extremal dependence	pt_PT
dc.subject	Spatial extremal index	pt_PT
dc.title	Clustering of high values in random fields	pt_PT
dc.type	journal article
dspace.entity.type	Publication
oaire.citation.endPage	838	pt_PT
oaire.citation.issue	4	pt_PT
oaire.citation.startPage	807	pt_PT
oaire.citation.volume	20	pt_PT
person.familyName	Pereira
person.familyName	ANDRÉ MARTINS FERNANDES
person.familyName	Ferreira
person.givenName	Luísa
person.givenName	ANA PAULA
person.givenName	Helena
person.identifier.ciencia-id	4F15-1868-D001
person.identifier.ciencia-id	C51F-68CB-1DE2
person.identifier.ciencia-id	7C10-8C72-313B
person.identifier.orcid	0000-0002-9068-4607
person.identifier.orcid	0000-0002-3908-821X
person.identifier.orcid	0000-0001-9392-7259
person.identifier.scopus-author-id	10839238300
person.identifier.scopus-author-id	7101834831
rcaap.rights	openAccess	pt_PT
rcaap.type	article	pt_PT
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