Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function

Handle URI:
http://hdl.handle.net/10754/625682
Title:
Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function
Authors:
Yan, Yuan; Genton, Marc G. ( 0000-0001-6467-2998 )
Abstract:
Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Yan Y, Genton MG (2017) Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function. Environmetrics: e2458. Available: http://dx.doi.org/10.1002/env.2458.
Publisher:
Wiley-Blackwell
Journal:
Environmetrics
Issue Date:
13-Jul-2017
DOI:
10.1002/env.2458
Type:
Article
ISSN:
1180-4009
Sponsors:
This research was supported by the King Abdullah University of Science and Technology (KAUST).
Additional Links:
http://onlinelibrary.wiley.com/doi/10.1002/env.2458/abstract
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorYan, Yuanen
dc.contributor.authorGenton, Marc G.en
dc.date.accessioned2017-10-03T12:49:33Z-
dc.date.available2017-10-03T12:49:33Z-
dc.date.issued2017-07-13en
dc.identifier.citationYan Y, Genton MG (2017) Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function. Environmetrics: e2458. Available: http://dx.doi.org/10.1002/env.2458.en
dc.identifier.issn1180-4009en
dc.identifier.doi10.1002/env.2458en
dc.identifier.urihttp://hdl.handle.net/10754/625682-
dc.description.abstractGaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.en
dc.description.sponsorshipThis research was supported by the King Abdullah University of Science and Technology (KAUST).en
dc.publisherWiley-Blackwellen
dc.relation.urlhttp://onlinelibrary.wiley.com/doi/10.1002/env.2458/abstracten
dc.subjectGaussian likelihooden
dc.subjectheavy tailsen
dc.subjectkrigingen
dc.subjectlog-Gaussian random fielden
dc.subjectMatérn covariance functionen
dc.subjectnon-Gaussian random fielden
dc.subjectskewnessen
dc.subjectspatial statisticsen
dc.subjectTukey g-and-h random fielden
dc.titleGaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance functionen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalEnvironmetricsen
kaust.authorYan, Yuanen
kaust.authorGenton, Marc G.en
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