Norm-dependent covariance permissibility of weakly homogeneous spatial random fields and its consequences in spatial statistics

Christakos, G; Papanicolaou, V

dc.contributor.author	Christakos, G	en
dc.contributor.author	Papanicolaou, V	en
dc.date.accessioned	2014-03-01T01:15:44Z
dc.date.available	2014-03-01T01:15:44Z
dc.date.issued	2000	en
dc.identifier.issn	1436-3240	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13700
dc.subject	random fields	en
dc.subject	norm	en
dc.subject	covariance	en
dc.subject	permissibility	en
dc.subject	estimation	en
dc.subject.classification	Engineering, Environmental	en
dc.subject.classification	Engineering, Civil	en
dc.subject.classification	Environmental Sciences	en
dc.subject.classification	Statistics & Probability	en
dc.subject.classification	Water Resources	en
dc.title	Norm-dependent covariance permissibility of weakly homogeneous spatial random fields and its consequences in spatial statistics	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s004770070001	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s004770070001	en
heal.language	English	en
heal.publicationDate	2000	en
heal.abstract	Permissibility of a covariance function (in the sense of Bochner) depends on the norm (or metric) that determines spatial distance in several dimensions. A covariance function that is permissible for one norm may not be so for another. We prove that for a certain class of covariances of weakly homogeneous random fields, the spatial distance can be defined only in terms of the Euclidean norm. This class includes commonly used covariance functions. Functions that do not belong to this class may be permissible covariances for some non-Euclidean metric. Thus, a different class of covariances, for which non-Euclidean norms are valid spatial distances, is also discussed. The choice of a coordinate system and associated norm to describe a physical phenomenon depends on the nature of the properties being described. Norm-dependent permissibility analysis has important consequences in spatial statistics applications (e.g., spatial estimation or mapping), in which one is concerned about the validity of covariance functions associated with a physically meaningful norm (Euclidean or non-Euclidean).	en
heal.publisher	SPRINGER-VERLAG	en
heal.journalName	STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT	en
dc.identifier.doi	10.1007/s004770070001	en
dc.identifier.isi	ISI:000165602700006	en
dc.identifier.volume	14	en
dc.identifier.issue	6	en
dc.identifier.spage	471	en
dc.identifier.epage	478	en