A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components

Handle URI:
http://hdl.handle.net/10754/597434
Title:
A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components
Authors:
Apanasovich, Tatiyana V.; Genton, Marc G.; Sun, Ying
Abstract:
We introduce a valid parametric family of cross-covariance functions for multivariate spatial random fields where each component has a covariance function from a well-celebrated Matérn class. Unlike previous attempts, our model indeed allows for various smoothnesses and rates of correlation decay for any number of vector components.We present the conditions on the parameter space that result in valid models with varying degrees of complexity. We discuss practical implementations, including reparameterizations to reflect the conditions on the parameter space and an iterative algorithm to increase the computational efficiency. We perform various Monte Carlo simulation experiments to explore the performances of our approach in terms of estimation and cokriging. The application of the proposed multivariate Matérnmodel is illustrated on two meteorological datasets: temperature/pressure over the Pacific Northwest (bivariate) and wind/temperature/pressure in Oklahoma (trivariate). In the latter case, our flexible trivariate Matérn model is valid and yields better predictive scores compared with a parsimonious model with common scale parameters. © 2012 American Statistical Association.
Citation:
Apanasovich TV, Genton MG, Sun Y (2012) A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components. Journal of the American Statistical Association 107: 180–193. Available: http://dx.doi.org/10.1080/01621459.2011.643197.
Publisher:
Informa UK Limited
Journal:
Journal of the American Statistical Association
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Mar-2012
DOI:
10.1080/01621459.2011.643197
Type:
Article
ISSN:
0162-1459; 1537-274X
Sponsors:
This publication is based in part on work supported by award no. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST) and by NSF grants DMS-1007504 and DMS-0707106. The authors thank the editor, two referees, and Tilmann Gneiting for their helpful comments and suggestions.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorApanasovich, Tatiyana V.en
dc.contributor.authorGenton, Marc G.en
dc.contributor.authorSun, Yingen
dc.date.accessioned2016-02-25T12:33:10Zen
dc.date.available2016-02-25T12:33:10Zen
dc.date.issued2012-03en
dc.identifier.citationApanasovich TV, Genton MG, Sun Y (2012) A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components. Journal of the American Statistical Association 107: 180–193. Available: http://dx.doi.org/10.1080/01621459.2011.643197.en
dc.identifier.issn0162-1459en
dc.identifier.issn1537-274Xen
dc.identifier.doi10.1080/01621459.2011.643197en
dc.identifier.urihttp://hdl.handle.net/10754/597434en
dc.description.abstractWe introduce a valid parametric family of cross-covariance functions for multivariate spatial random fields where each component has a covariance function from a well-celebrated Matérn class. Unlike previous attempts, our model indeed allows for various smoothnesses and rates of correlation decay for any number of vector components.We present the conditions on the parameter space that result in valid models with varying degrees of complexity. We discuss practical implementations, including reparameterizations to reflect the conditions on the parameter space and an iterative algorithm to increase the computational efficiency. We perform various Monte Carlo simulation experiments to explore the performances of our approach in terms of estimation and cokriging. The application of the proposed multivariate Matérnmodel is illustrated on two meteorological datasets: temperature/pressure over the Pacific Northwest (bivariate) and wind/temperature/pressure in Oklahoma (trivariate). In the latter case, our flexible trivariate Matérn model is valid and yields better predictive scores compared with a parsimonious model with common scale parameters. © 2012 American Statistical Association.en
dc.description.sponsorshipThis publication is based in part on work supported by award no. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST) and by NSF grants DMS-1007504 and DMS-0707106. The authors thank the editor, two referees, and Tilmann Gneiting for their helpful comments and suggestions.en
dc.publisherInforma UK Limiteden
dc.subjectCokrigingen
dc.subjectCorrelation decayen
dc.subjectMultivariateen
dc.subjectSmoothnessen
dc.subjectSpatialen
dc.subjectValid cross-covarianceen
dc.titleA Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Componentsen
dc.typeArticleen
dc.identifier.journalJournal of the American Statistical Associationen
dc.contributor.institutionThomas Jefferson University, Philadelphia, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionStatistical and Applied Mathematical Sciences Institute, USA, Research Triangle Park, United Statesen
kaust.grant.numberKUS-C1-016-04en
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