Estimating varying coefficients for partial differential equation models

Zhang, X; Cao, J; Carroll, RJ

Estimating varying coefficients for partial differential equation models

Zhang, X Cao, J Carroll, RJ

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Publication Type:: Journal Article
Citation:: Biometrics, 2017, 73 (3), pp. 949 - 959
Issue Date:: 2017-09-01

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Field	Value	Language
dc.contributor.author	Zhang, X	en_US
dc.contributor.author	Cao, J	en_US
dc.contributor.author	Carroll, RJ https://orcid.org/0000-0002-5465-9682	en_US
dc.date.available	2016-12-01	en_US
dc.date.issued	2017-09-01	en_US
dc.identifier.citation	Biometrics, 2017, 73 (3), pp. 949 - 959	en_US
dc.identifier.issn	0006-341X	en_US
dc.identifier.uri	http://hdl.handle.net/10453/127240
dc.description.abstract	© 2017, The International Biometric Society Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data.	en_US
dc.relation.ispartof	Biometrics	en_US
dc.relation.isbasedon	10.1111/biom.12646	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.subject.mesh	Models, Theoretical	en_US
dc.subject.mesh	Computer Simulation	en_US
dc.title	Estimating varying coefficients for partial differential equation models	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	73	en_US
utslib.for	0104 Statistics	en_US
utslib.for	0199 Other Mathematical Sciences	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.issue	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	73	en_US

Abstract:

© 2017, The International Biometric Society Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data.

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http://hdl.handle.net/10453/127240