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Subject-wise empirical likelihood inference in partial linear models for longitudinal data

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  • Qian, Lianfen
  • Wang, Suojin

Abstract

In analyzing longitudinal data, within-subject correlations are a major factor that affects statistical efficiency. Working with a partially linear model for longitudinal data, a subject-wise empirical likelihood based method that takes the within-subject correlations into consideration is proposed to estimate the model parameters. A nonparametric version of the Wilks Theorem for the limiting distribution of the empirical likelihood ratio, which relies on a kernel regression smoothing method to properly centered data, is derived. The estimation of the nonparametric baseline function is also considered. A simulation study and an application are reported to investigate the finite sample properties of the proposed method. The numerical results demonstrate the usefulness of the proposed method.

Suggested Citation

  • Qian, Lianfen & Wang, Suojin, 2017. "Subject-wise empirical likelihood inference in partial linear models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 77-87.
    • Handle: RePEc:eee:csdana:v:111:y:2017:i:c:p:77-87
    DOI: 10.1016/j.csda.2017.02.001
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    References listed on IDEAS

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    1. Suojin Wang & Lianfen Qian & Raymond J. Carroll, 2010. "Generalized empirical likelihood methods for analyzing longitudinal data," Biometrika, Biometrika Trust, vol. 97(1), pages 79-93.
    2. You-Gan Wang, 2003. "Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance," Biometrika, Biometrika Trust, vol. 90(1), pages 29-41, March.
    3. Fan, Jianqing & Wu, Yichao, 2008. "Semiparametric Estimation of Covariance Matrixes for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1520-1533.
    4. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    5. Liugen Xue & Lixing Zhu, 2007. "Empirical Likelihood Semiparametric Regression Analysis for Longitudinal Data," Biometrika, Biometrika Trust, vol. 94(4), pages 921-937.
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    Cited by:

    1. Caiya Zhang & Kaihong Xu & Lianfen Qian, 2020. "Asymptotic properties of the QMLE in a log-linear RealGARCH model with Gaussian errors," Statistical Papers, Springer, vol. 61(6), pages 2313-2330, December.
    2. Amelia Simó & M. Victoria Ibáñez & Irene Epifanio & Vicent Gimeno, 2020. "Generalized partially linear models on Riemannian manifolds," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(3), pages 641-661, June.

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