Kernel-Based Profile Estimation for Ordinary Differential Equations with Partially Measured State Variables

Kernel-based profile estimation (KBPE) is proposed for the partially measured ODEs. Compared to the existing approaches the structure information contained in ODEs is used more efficiently in KBPE and no higher order derivatives need to be estimated form the measurements. Construction of confidence interval in finite samples setting for both parameters and state variables are also discussed. Simulation studies show that KBPE can estimate the partially measured ODEs reasonably when the ordinary two-step approach cannot apply. We also illustrate KBPE by a real data set from a clinical HIV study.