Estimating varying coefficients for partial differential equation models. Academic Article

abstract

• 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.

authors

• Carroll, Raymond

published proceedings

• Biometrics

author list (cited authors)

• Zhang, X., Cao, J., & Carroll, R. J.

citation count

• 3

complete list of authors

• Zhang, Xinyu||Cao, Jiguo||Carroll, Raymond J

publication date

• September 2017

publisher

• Wiley  Publisher

published in

• Biometrics  Journal

keywords

• B-splines
• Computer Simulation
• Dynamical Models
• Inverse Problems
• Lidar Data
• Models, Theoretical
• Parameter Cascading
• System Identification

PubMed Central ID

• 28076654

Digital Object Identifier (DOI)

• 10.1111/biom.12646

start page

• 949

end page

• 959

volume

• 73

issue

• 3

URL

• http%3A%2F%2Fdx.doi.org%2F10.1111%2Fbiom.12646