title: Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression.
abstract: We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method.
authors.affiliation: Department of Mathematics, Northeastern University, 360 Huntington Ave., Boston, MA 02115, U.S.A.
authors.forename: A Adam
authors.initials: AA
authors.lastname: Ding
authors.affiliation: Department of Biostatistics and Computational Biology, University of Rochester School of Medicine and Dentistry, 601 Elmwood Avenue, Box 630, Rochester, New York 14642, U.S.A.
authors.forename: Hulin
authors.initials: H
authors.lastname: Wu
keywords: Constrained optimization; Local polynomial smoothing; Ordinary differential equation