title: Estimating varying coefficients for partial differential equation models.
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.affiliation: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and Statistics and Mathematics College, Yunnan University of Finance and Economics, Kunming 650221, China.
authors.forename: Xinyu
authors.initials: X
authors.lastname: Zhang
authors.affiliation: Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, British Columbia, V5A1S6, Canada.
authors.forename: Jiguo
authors.initials: J
authors.lastname: Cao
authors.affiliation: Department of Statistics, Texas A&M University, 3143 TAMU, College Station, Texas 77843-3143, U.S.A.|School of Mathematical and Physical Sciences, University of Technology, Sydney, PO Box 123, Broadway, New South Wales 2007, Australia.
authors.forename: Raymond J
authors.initials: RJ
authors.lastname: Carroll
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical
keywords: B-splines; Dynamical models; Inverse problems; LIDAR data; Parameter cascading; System identification