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Inferences in semi-parametric dynamic mixed models for longitudinal count data

Author

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  • Nan Zheng

    (Memorial University)

  • Brajendra C. Sutradhar

    (Memorial University)

Abstract

This paper considers a semi-parametric mixed model for longitudinal counts under the assumption that for conditional on a common random effect over time the repeated count responses of an individual follow a Poisson AR(1) (auto-regressive order 1) non-stationary correlation structure. A step-by-step estimation approach is developed which provides consistent estimators for the non-parametric function, regression parameters, variance of the random effects, and auto-correlation structure of the model. Proofs for the consistency properties of the estimators along with their convergence rates are derived. A simulation study is conducted to examine first the estimation effects on parameters when the non-parametric function is ignored, and then an overall estimation study is carried out in the presence of the non-parametric function by including its estimation as well.

Suggested Citation

  • Nan Zheng & Brajendra C. Sutradhar, 2018. "Inferences in semi-parametric dynamic mixed models for longitudinal count data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 215-247, February.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:1:d:10.1007_s10463-016-0590-9
    DOI: 10.1007/s10463-016-0590-9
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    References listed on IDEAS

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    1. Montalvo, Jose G, 1997. "GMM Estimation of Count-Panel-Data Models with Fixed Effects and Predetermined Instruments," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 82-89, January.
    2. Lin X. & Carroll R. J., 2001. "Semiparametric Regression for Clustered Data Using Generalized Estimating Equations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1045-1056, September.
    3. Rainer Winkelmann, 2008. "Econometric Analysis of Count Data," Springer Books, Springer, edition 0, number 978-3-540-78389-3, March.
    4. Wooldridge, Jeffrey M., 1999. "Distribution-free estimation of some nonlinear panel data models," Journal of Econometrics, Elsevier, vol. 90(1), pages 77-97, May.
    5. Sneddon, Gary & Sutradhar, Brajendra C., 2004. "On semiparametric familial-longitudinal models," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 369-379, September.
    6. Xihong Lin & Raymond J. Carroll, 2006. "Semiparametric estimation in general repeated measures problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 69-88, February.
    7. Cinzia Carota, 2002. "Semiparametric regression for count data," Biometrika, Biometrika Trust, vol. 89(2), pages 265-281, June.
    8. Jeng‐Min Chiou & Hans‐Georg Müller, 2005. "Estimated estimating equations: semiparametric inference for clustered and longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 531-553, September.
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    Cited by:

    1. Nan Zheng & Noel Cadigan, 2025. "Improved confidence intervals for nonlinear mixed-effects and nonparametric regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(1), pages 105-126, February.

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