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Partial Linear Models for Longitudinal Data Based on Quadratic Inference Functions

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  • YANG BAI
  • ZHONGYI ZHU
  • WING K. FUNG

Abstract

In this paper, we consider improved estimating equations for semiparametric partial linear models (PLM) for longitudinal data, or clustered data in general. We approximate the non‐parametric function in the PLM by a regression spline, and utilize quadratic inference functions (QIF) in the estimating equations to achieve a more efficient estimation of the parametric part in the model, even when the correlation structure is misspecified. Moreover, we construct a test which is an analogue to the likelihood ratio inference function for inferring the parametric component in the model. The proposed methods perform well in simulation studies and real data analysis conducted in this paper.

Suggested Citation

  • Yang Bai & Zhongyi Zhu & Wing K. Fung, 2008. "Partial Linear Models for Longitudinal Data Based on Quadratic Inference Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(1), pages 104-118, March.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:1:p:104-118
    DOI: 10.1111/j.1467-9469.2007.00578.x
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    Cited by:

    1. Li, Daoji & Pan, Jianxin, 2013. "Empirical likelihood for generalized linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 63-73.
    2. Tian, Ruiqin & Xue, Liugen & Xu, Dengke, 2016. "Automatic variable selection for varying coefficient models with longitudinal data," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 84-90.
    3. Tian, Ruiqin & Xue, Liugen & Liu, Chunling, 2014. "Penalized quadratic inference functions for semiparametric varying coefficient partially linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 94-110.
    4. Lai, Peng & Li, Gaorong & Lian, Heng, 2013. "Quadratic inference functions for partially linear single-index models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 115-127.
    5. Kangning Wang & Mengjie Hao & Xiaofei Sun, 2021. "Robust and efficient estimating equations for longitudinal data partial linear models and its applications," Statistical Papers, Springer, vol. 62(5), pages 2147-2168, October.
    6. Bai, Yang & Fung, Wing K. & Zhu, Zhong Yi, 2009. "Penalized quadratic inference functions for single-index models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 152-161, January.
    7. Zhao, Weihua & Lian, Heng & Song, Xinyuan, 2017. "Composite quantile regression for correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 15-33.

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