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Time-varying coefficient estimation in differential equation models with noisy time-varying covariates

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  • Hong, Zhaoping
  • Lian, Heng

Abstract

We study the problem of estimating time-varying coefficients in ordinary differential equations. Current theory only applies to the case when the associated state variables are observed without measurement errors as presented in Chen and Wu (2008)Â [4] and [5]. The difficulty arises from the quadratic functional of observations that one needs to deal with instead of the linear functional that appears when state variables contain no measurement errors. We derive the asymptotic bias and variance for the previously proposed two-step estimators using quadratic regression functional theory.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:103:y:2012:i:1:p:58-67
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    References listed on IDEAS

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    1. Chen, Jianwei & Wu, Hulin, 2008. "Efficient Local Estimation for Time-Varying Coefficients in Deterministic Dynamic Models With Applications to HIV-1 Dynamics," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 369-384, March.
    2. Hongyu Miao & Carrie Dykes & Lisa M. Demeter & Hulin Wu, 2009. "Differential Equation Modeling of HIV Viral Fitness Experiments: Model Identification, Model Selection, and Multimodel Inference," Biometrics, The International Biometric Society, vol. 65(1), pages 292-300, March.
    3. Wenqin Pan & Donglin Zeng & Xihong Lin, 2009. "Estimation in Semiparametric Transition Measurement Error Models for Longitudinal Data," Biometrics, The International Biometric Society, vol. 65(3), pages 728-736, September.
    4. 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.
    5. J. O. Ramsay & G. Hooker & D. Campbell & J. Cao, 2007. "Parameter estimation for differential equations: a generalized smoothing approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 741-796, November.
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    Cited by:

    1. Apergis, Nicholas & Polemis, Michael, 2018. "Electricity supply shocks and economic growth across the US states: evidence from a time-varying Bayesian panel VAR model, aggregate and disaggregate energy sources," MPRA Paper 84954, University Library of Munich, Germany.

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