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Efficient semiparametric regression for longitudinal data with regularised estimation of error covariance function

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  • Shengji Jia
  • Chunming Zhang
  • Hulin Wu

Abstract

Improving estimation efficiency for regression coefficients is an important issue in the analysis of longitudinal data, which involves estimating the covariance matrix of errors. But challenges arise in estimating the covariance matrix of longitudinal data collected at irregular or unbalanced time points. In this paper, we develop a regularisation method for estimating the covariance function and a stepwise procedure for estimating the parametric components efficiently in the varying-coefficient partially linear model. This procedure is also applicable to the varying-coefficient temporal mixed-effects model. Our method utilises the structure of the covariance function and thus has faster rates of convergence in estimating the covariance functions and outperforms the existing approaches in simulation studies. This procedure is easy to implement and its numerical performance is investigated using both simulated and real data.

Suggested Citation

  • Shengji Jia & Chunming Zhang & Hulin Wu, 2019. "Efficient semiparametric regression for longitudinal data with regularised estimation of error covariance function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(4), pages 867-886, October.
    • Handle: RePEc:taf:gnstxx:v:31:y:2019:i:4:p:867-886
    DOI: 10.1080/10485252.2019.1651853
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    Cited by:

    1. Jia, Shengji & Zhang, Chunming & Lu, Haoran, 2022. "Covariance function versus covariance matrix estimation in efficient semi-parametric regression for longitudinal data analysis," Journal of Multivariate Analysis, Elsevier, vol. 187(C).

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