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Estimating Varying Coefficients for Partial Differential Equation Models
Zhang, Xinyu1,2; Cao, Jiguo3; Carroll, Raymond J.4,5
2017-09-01
Source PublicationBIOMETRICS
ISSN0006-341X
Volume73Issue:3Pages:949-959
AbstractPartial 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.
KeywordB-splines Dynamical models Inverse problems LIDAR data Parameter cascading System identification
DOI10.1111/biom.12646
Language英语
WOS Research AreaLife Sciences & Biomedicine - Other Topics ; Mathematical & Computational Biology ; Mathematics
WOS SubjectBiology ; Mathematical & Computational Biology ; Statistics & Probability
WOS IDWOS:000411878000026
PublisherWILEY
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26666
Collection系统科学研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Yunnan Univ Finance & Econ, Stat & Math Coll, Kunming 650221, Yunnan, Peoples R China
3.Simon Fraser Univ, Dept Stat & Actuarial Sci, Burnaby, BC V5A 1S6, Canada
4.Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA
5.Univ Technol, Sch Math & Phys Sci, POB 123, Broadway, NSW 2007, Australia
Recommended Citation
GB/T 7714
Zhang, Xinyu,Cao, Jiguo,Carroll, Raymond J.. Estimating Varying Coefficients for Partial Differential Equation Models[J]. BIOMETRICS,2017,73(3):949-959.
APA Zhang, Xinyu,Cao, Jiguo,&Carroll, Raymond J..(2017).Estimating Varying Coefficients for Partial Differential Equation Models.BIOMETRICS,73(3),949-959.
MLA Zhang, Xinyu,et al."Estimating Varying Coefficients for Partial Differential Equation Models".BIOMETRICS 73.3(2017):949-959.
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