Statistically and Computationally Efficient Estimating Equations for Large Spatial Datasets

Handle URI:
http://hdl.handle.net/10754/552300
Title:
Statistically and Computationally Efficient Estimating Equations for Large Spatial Datasets
Authors:
Sun, Ying ( 0000-0001-6703-4270 ) ; Stein, Michael L.
Abstract:
For Gaussian process models, likelihood based methods are often difficult to use with large irregularly spaced spatial datasets, because exact calculations of the likelihood for n observations require O(n3) operations and O(n2) memory. Various approximation methods have been developed to address the computational difficulties. In this paper, we propose new unbiased estimating equations based on score equation approximations that are both computationally and statistically efficient. We replace the inverse covariance matrix that appears in the score equations by a sparse matrix to approximate the quadratic forms, then set the resulting quadratic forms equal to their expected values to obtain unbiased estimating equations. The sparse matrix is constructed by a sparse inverse Cholesky approach to approximate the inverse covariance matrix. The statistical efficiency of the resulting unbiased estimating equations are evaluated both in theory and by numerical studies. Our methods are applied to nearly 90,000 satellite-based measurements of water vapor levels over a region in the Southeast Pacific Ocean.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Statistically and Computationally Efficient Estimating Equations for Large Spatial Datasets 2014:00 Journal of Computational and Graphical Statistics
Publisher:
Informa UK Limited
Journal:
Journal of Computational and Graphical Statistics
Issue Date:
7-Nov-2014
DOI:
10.1080/10618600.2014.975230
Type:
Article
ISSN:
1061-8600; 1537-2715
Additional Links:
http://www.tandfonline.com/doi/abs/10.1080/10618600.2014.975230
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSun, Yingen
dc.contributor.authorStein, Michael L.en
dc.date.accessioned2015-05-05T14:28:40Zen
dc.date.available2015-05-05T14:28:40Zen
dc.date.issued2014-11-07en
dc.identifier.citationStatistically and Computationally Efficient Estimating Equations for Large Spatial Datasets 2014:00 Journal of Computational and Graphical Statisticsen
dc.identifier.issn1061-8600en
dc.identifier.issn1537-2715en
dc.identifier.doi10.1080/10618600.2014.975230en
dc.identifier.urihttp://hdl.handle.net/10754/552300en
dc.description.abstractFor Gaussian process models, likelihood based methods are often difficult to use with large irregularly spaced spatial datasets, because exact calculations of the likelihood for n observations require O(n3) operations and O(n2) memory. Various approximation methods have been developed to address the computational difficulties. In this paper, we propose new unbiased estimating equations based on score equation approximations that are both computationally and statistically efficient. We replace the inverse covariance matrix that appears in the score equations by a sparse matrix to approximate the quadratic forms, then set the resulting quadratic forms equal to their expected values to obtain unbiased estimating equations. The sparse matrix is constructed by a sparse inverse Cholesky approach to approximate the inverse covariance matrix. The statistical efficiency of the resulting unbiased estimating equations are evaluated both in theory and by numerical studies. Our methods are applied to nearly 90,000 satellite-based measurements of water vapor levels over a region in the Southeast Pacific Ocean.en
dc.publisherInforma UK Limiteden
dc.relation.urlhttp://www.tandfonline.com/doi/abs/10.1080/10618600.2014.975230en
dc.rightsThis is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Computational and Graphical Statistics on Nov 07 2014, available online: http://www.tandfonline.com/doi/abs/10.1080/10618600.2014.975230.en
dc.subjectInverse covariance matrixen
dc.subjectIterative methodsen
dc.subjectSparse matricesen
dc.subjectStatistical efficiencyen
dc.subjectUnbiased estimating equationsen
dc.titleStatistically and Computationally Efficient Estimating Equations for Large Spatial Datasetsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalJournal of Computational and Graphical Statisticsen
dc.eprint.versionPost-printen
dc.contributor.institutionDepartment of Statistics, University of Chicago, Chicago, IL, 60637en
kaust.authorSun, Yingen
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