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Generalized Ordinary Differential Equation Models

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  • Hongyu Miao
  • Hulin Wu
  • Hongqi Xue

Abstract

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method. Supplementary materials for this article are available online.

Suggested Citation

  • Hongyu Miao & Hulin Wu & Hongqi Xue, 2014. "Generalized Ordinary Differential Equation Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1672-1682, December.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:508:p:1672-1682
    DOI: 10.1080/01621459.2014.957287
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    1. Bo-Cheng Wei & Jian-Qing Shi & Wing-Kam Fung & Yue-Qing Hu, 1998. "Testing for Varying Dispersion in Exponential Family Nonlinear Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 277-294, June.
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    Cited by:

    1. Nanshan, Muye & Zhang, Nan & Xun, Xiaolei & Cao, Jiguo, 2022. "Dynamical modeling for non-Gaussian data with high-dimensional sparse ordinary differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    2. Xinyu Zhang & Jiguo Cao & Raymond J. Carroll, 2017. "Estimating varying coefficients for partial differential equation models," Biometrics, The International Biometric Society, vol. 73(3), pages 949-959, September.
    3. Xuming Tong & Jinghang Chen & Hongyu Miao & Tingting Li & Le Zhang, 2015. "Development of an Agent-Based Model (ABM) to Simulate the Immune System and Integration of a Regression Method to Estimate the Key ABM Parameters by Fitting the Experimental Data," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-14, November.

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