A Generalized Smoother for Linear Ordinary Differential Equations

ABSTRACT

Ordinary differential equations (ODEs) are equalities involving a function and its derivatives that define the evolution of the function over a prespecified domain. The applications of ODEs range from simulation and prediction to control and diagnosis in diverse fields such as engineering, physics, medicine, and finance. Parameter estimation is often required to calibrate these theoretical models to data. While there are many methods for estimating ODE parameters from partially observed data, they are invariably subject to several problems including high computational cost, complex estimation procedures, biased estimates, and large sampling variance. We propose a method that overcomes these issues and produces estimates of the ODE parameters that have less bias, a smaller sampling variance, and a 10-fold improvement in computational efficiency. The package GenPen containing the Matlab code to perform the methods described in this article is available online.

Keywords:

• B-splines
• Functional data analysis
• Model-based penalized regression

Supplementary Materials

Matlab-package for Generalized smoothing algorithm: Matlab-package GenPen containing code to perform the generalized smoothing of linear ODEs as described in the article. The package also contains all datasets used as examples in the article. (GNU zipped tar file)