題　目：Regularized Estimation for Ordinary Differential Equations: An Alternative View on Penalty and beyond 主講人：Prof. Naisyin Wang (University of Michigan, USA) 時　間：101年4月30日(星期一)下午13:30-14:20 地　點：交大綜合一館427室 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 (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 manuscript, we take an alternative view through variance/stability 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. 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 eliminate this problem. We observe this phenomenon in a numerical study even when the underlying ordinary differential equations model is mis-specified. This recognition enables us to address the goodness of fit problems by considering regularization procedure with a more flexible parameter structures across a long period of study time, and 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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