期刊
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
卷 21, 期 1, 页码 42-56出版社
TAYLOR & FRANCIS INC
DOI: 10.1198/jcgs.2011.10021
关键词
Dynamic models; Function estimation; Penalized splines
资金
- Natural Science and Engineering Research Council of Canada (NSERC)
- NCI [CA57030]
- NSF [DMS-0907170]
- King Abdullah University of Science and Technology (KAUST) [KUS-CI-016-04]
- NIH/NIAID
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0907170] Funding Source: National Science Foundation
Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.
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