Parameter Estimation for Ordinary Differential Equations: An Alternative View on Penalty

• Activity Number: 410
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yun Li*+
• Companies: University of Michigan
• Keywords: Penalty parameter ; predator-prey data ; profile estimation ; smoothing ; spline-basis

Abstract

Dynamic modeling through solving ordinary differential equations has ample applications in many fields. The recently proposed parameter-cascades estimation procedure with a penalized estimation component (Ramsay et al., 2007) combines the strengths of basis-function approximation, profile-based estimation and computation feasibility. Consequently, it has become a very popular estimation procedure. In this paper, we take an alternative view through variance evaluation on the penalized estimation component within the parameter-cascades procedure. We found that the penalty term in the profile component could increase estimation variation. Further, contrary to the traditional belief established from the penalized spline literature, this penalty term in the ordinary differential equations setup also makes the procedure more sensitive to the number of basis functions. By taking the penalty parameter to its limit, we propose an alternative estimation procedure. The simulation studies indicate that our proposed method outperforms the popular penalty-based method, and in real data analysis two methods give similar outcomes. We also provide theoretical properties for the proposed estimator.