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Parameter Estimation for Differential Equation Models Using a Framework of Measurement Error in Regression Models

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  • Liang, Hua
  • Wu, Hulin

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  • Liang, Hua & Wu, Hulin, 2008. "Parameter Estimation for Differential Equation Models Using a Framework of Measurement Error in Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1570-1583.
    • Handle: RePEc:bes:jnlasa:v:103:i:484:y:2008:p:1570-1583
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    Cited by:

    1. Hanwen Huang, 2022. "Bayesian multi‐level mixed‐effects model for influenza dynamics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1978-1995, November.
    2. Ying Zhu, 2021. "Phase transitions in nonparametric regressions," Papers 2112.03626, arXiv.org, revised Nov 2023.
    3. Hulin Wu & Hongqi Xue & Arun Kumar, 2012. "Numerical Discretization-Based Estimation Methods for Ordinary Differential Equation Models via Penalized Spline Smoothing with Applications in Biomedical Research," Biometrics, The International Biometric Society, vol. 68(2), pages 344-352, June.
    4. 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).
    5. Hao, Siteng & Lin, Shu-Chin & Wang, Jane-Ling & Zhong, Qixian, 2024. "Dynamic modeling for multivariate functional and longitudinal data," Journal of Econometrics, Elsevier, vol. 239(2).
    6. Baisen Liu & Liangliang Wang & Yunlong Nie & Jiguo Cao, 2021. "Semiparametric Mixed-Effects Ordinary Differential Equation Models with Heavy-Tailed Distributions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 428-445, September.
    7. Tao Lu & Yangxin Huang & Min Wang & Feng Qian, 2014. "A refined parameter estimating approach for HIV dynamic model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(8), pages 1645-1657, August.
    8. Shizhe Chen & Ali Shojaie & Daniela M. Witten, 2017. "Network Reconstruction From High-Dimensional Ordinary Differential Equations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1697-1707, October.
    9. Zhou, Jie & Han, Lu & Liu, Sanyang, 2013. "Nonlinear mixed-effects state space models with applications to HIV dynamics," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1448-1456.
    10. Ahn, Kwang Woo & Chan, Kung-Sik, 2014. "Approximate conditional least squares estimation of a nonlinear state-space model via an unscented Kalman filter," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 243-254.
    11. Hong, Zhaoping & Lian, Heng, 2012. "Time-varying coefficient estimation in differential equation models with noisy time-varying covariates," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 58-67, January.
    12. Mu Niu & Benn Macdonald & Simon Rogers & Maurizio Filippone & Dirk Husmeier, 2018. "Statistical inference in mechanistic models: time warping for improved gradient matching," Computational Statistics, Springer, vol. 33(2), pages 1091-1123, June.
    13. Van Kinh Nguyen & Frank Klawonn & Rafael Mikolajczyk & Esteban A Hernandez-Vargas, 2016. "Analysis of Practical Identifiability of a Viral Infection Model," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-16, December.
    14. Golchi, Shirin & Campbell, David A., 2016. "Sequentially Constrained Monte Carlo," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 98-113.
    15. Liu, Baisen & Wang, Liangliang & Nie, Yunlong & Cao, Jiguo, 2019. "Bayesian inference of mixed-effects ordinary differential equations models using heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 233-246.
    16. Zhou, Jie, 2015. "Detection of influential measurement for ordinary differential equation with application to HIV dynamics," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 324-332.
    17. Carey, M. & Ramsay, J.O., 2021. "Fast stable parameter estimation for linear dynamical systems," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    18. Strebel, Oliver, 2013. "A preprocessing method for parameter estimation in ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 93-104.
    19. Mu Niu & Joe Wandy & Rónán Daly & Simon Rogers & Dirk Husmeier, 2021. "R package for statistical inference in dynamical systems using kernel based gradient matching: KGode," Computational Statistics, Springer, vol. 36(1), pages 715-747, March.
    20. Bin Zhu & Peter X.-K. Song & Jeremy M.G. Taylor, 2011. "Stochastic Functional Data Analysis: A Diffusion Model-Based Approach," Biometrics, The International Biometric Society, vol. 67(4), pages 1295-1304, December.
    21. Hanwen Huang & Andreas Handel & Xiao Song, 2020. "A Bayesian approach to estimate parameters of ordinary differential equation," Computational Statistics, Springer, vol. 35(3), pages 1481-1499, September.

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