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

• Activity Number: 106
• Type: Invited
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Yun Li and Ji Zhu and Naisyin Wang*+
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: ODE ; Dynamic modeling ; penalty ; semiparametric

Abstract

Dynamic modeling through solving ordinary differential equations has ample applications in the fields of physics, engineering, economics and biological sciences. The recently proposed parameter-cascades estimation procedure with a penalized estimation component combines the strengths of basis-function approximation, profile-based estimation and computation feasibility. Consequently, it has become a very popular estimation procedure. In this manuscript, we take an alternative view through variance evaluation on the penalized estimation component within the parameter-cascades procedure. We found, through some theoretical evaluation and numerical experiments, that the penalty term in the profile component could increase estimation variation. This recognition lead us to address the goodness of fit problems by considering a more flexible parameter structures across a long period of study time by using an alternative penalty structure. In this talk, we will illustrate our findings on both theoretical and numerical aspects. This is joint work with Yun Li and Ji Zhu of University of Michigan.