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Nonparametric estimation of conditional distribution functions with longitudinal data and time-varying parametric models

Author

Listed:
  • Mohammed Chowdhury

    (KSU)

  • Colin Wu

    (Office of Biostatistics Research, NHLBI, NIH)

  • Reza Modarres

    (GWU)

Abstract

Nonparametric estimation and inferences of conditional distribution functions with longitudinal data have important applications in biomedical studies. We propose in this paper an estimation approach based on time-varying parametric models. Our model assumes that the conditional distribution of the outcome variable at each given time point can be approximated by a parametric model, but the parameters are smooth functions of time. Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the conditional distribution functions at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. Asymptotic properties, including the asymptotic biases, variances and mean squared errors, are derived for the local polynomial smoothed estimators. Applicability of our two-step estimation method is demonstrated through a large epidemiological study of childhood growth and blood pressure. Finite sample properties of our procedures are investigated through simulation study.

Suggested Citation

  • Mohammed Chowdhury & Colin Wu & Reza Modarres, 2018. "Nonparametric estimation of conditional distribution functions with longitudinal data and time-varying parametric models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 61-83, January.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:1:d:10.1007_s00184-017-0634-z
    DOI: 10.1007/s00184-017-0634-z
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    References listed on IDEAS

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    1. Colin Wu & Xin Tian & Jarvis Yu, 2010. "Nonparametric estimation for time-varying transformation models with longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 133-147.
    2. Zonghui Hu, 2004. "Profile-kernel versus backfitting in the partially linear models for longitudinal/clustered data," Biometrika, Biometrika Trust, vol. 91(2), pages 251-262, June.
    3. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    4. Lan Zhou & Jianhua Z. Huang & Raymond J. Carroll, 2008. "Joint modelling of paired sparse functional data using principal components," Biometrika, Biometrika Trust, vol. 95(3), pages 601-619.
    5. J. Fan & J.‐T. Zhang, 2000. "Two‐step estimation of functional linear models with applications to longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 303-322.
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