Estimating basis functions in massive fields under the spatial random effects model

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dc.contributor.author Pazdernik, Karl
dc.contributor.author Maitra, Ranjan
dc.contributor.department Statistics
dc.date 2020-06-23T04:15:22.000
dc.date.accessioned 2020-07-02T06:57:46Z
dc.date.available 2020-07-02T06:57:46Z
dc.date.copyright Wed Jan 01 00:00:00 UTC 2020
dc.date.issued 2020-01-01
dc.description.abstract <p>Spatial prediction is commonly achieved under the assumption of a Gaussian random field (GRF) by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets, fixed rank kriging using the Expectation-Maximization (EM) algorithm for estimation has been proposed as an alternative to the usual but computationally prohibitive kriging method. The method reduces computation cost of estimation by redefining the spatial process as a linear combination of basis functions and spatial random effects. A disadvantage of this method is that it imposes constraints on the relationship between the observed locations and the knots. We develop an alternative method that utilizes the Spatial Mixed Effects (SME) model, but allows for additional flexibility by estimating the range of the spatial dependence between the observations and the knots via an Alternating Expectation Conditional Maximization (AECM) algorithm. Experiments show that our methodology improves estimation without sacrificing prediction accuracy while also minimizing the additional computational burden of extra parameter estimation. The methodology is applied to a temperature data set archived by the United States National Climate Data Center, with improved results over previous methodology.</p>
dc.description.comments <p>This is a pre-print of the article Pazdernik, Karl T., and Ranjan Maitra. "Estimating Basis Functions in Massive Fields under the Spatial Mixed Effects Model." <em>arXiv preprint arXiv:2003.05990</em> (2020). Posted with permission.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/stat_las_pubs/304/
dc.identifier.articleid 1307
dc.identifier.contextkey 18213002
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath stat_las_pubs/304
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/90626
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/stat_las_pubs/304/2020_MaitraRanjan_EstimatingBasis.pdf|||Fri Jan 14 23:28:48 UTC 2022
dc.subject.disciplines Statistical Methodology
dc.subject.keywords kriging
dc.subject.keywords fixed rank kriging
dc.subject.keywords bandwidth
dc.subject.keywords range parameter
dc.subject.keywords basis functions
dc.subject.keywords maximum likelihood estimation
dc.subject.keywords Alternating Expectation Conditional Maximization algorithm
dc.title Estimating basis functions in massive fields under the spatial random effects model
dc.type article
dc.type.genre article
dspace.entity.type Publication
relation.isOrgUnitOfPublication 264904d9-9e66-4169-8e11-034e537ddbca
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