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Activity Number: 106
Type: Invited
Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #303891
Title: Parameter Estimation for Ordinary Differential Equations: An Alternative View on Penalty
Author(s): Yun Li and Ji Zhu and Naisyin Wang*+
Companies: University of Michigan and University of Michigan and University of Michigan
Address: Department of Statistics. 439 West Hall, 1085 South University Ave., Ann Arbor, MI, , USA
Keywords: ODE ; Dynamic modeling ; penalty ; semiparametric

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.

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