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Efficient Estimation of the Nonparametric Mean and Covariance Functions for Longitudinal and Sparse Functional Data

Author

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  • Ling Zhou
  • Huazhen Lin
  • Hua Liang

Abstract

We consider the estimation of mean and covariance functions for longitudinal and sparse functional data by using the full quasi-likelihood coupling a modification of the local kernel smoothing method. The proposed estimators are shown to be consistent, asymptotically normal, and semiparametrically efficient in terms of their linear functionals. Their superiority to the competitors is further illustrated numerically through simulation studies. The method is applied to analyze AIDS study and atmospheric study. Supplementary materials for this article are available online.

Suggested Citation

  • Ling Zhou & Huazhen Lin & Hua Liang, 2018. "Efficient Estimation of the Nonparametric Mean and Covariance Functions for Longitudinal and Sparse Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1550-1564, October.
    • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:524:p:1550-1564
    DOI: 10.1080/01621459.2017.1356317
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    Cited by:

    1. Zhong, Rou & Liu, Shishi & Li, Haocheng & Zhang, Jingxiao, 2022. "Robust functional principal component analysis for non-Gaussian longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Yuliana Linke & Igor Borisov & Pavel Ruzankin & Vladimir Kutsenko & Elena Yarovaya & Svetlana Shalnova, 2024. "Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Uniform Consistency," Mathematics, MDPI, vol. 12(12), pages 1-23, June.
    3. Yuliana Linke & Igor Borisov & Pavel Ruzankin & Vladimir Kutsenko & Elena Yarovaya & Svetlana Shalnova, 2022. "Universal Local Linear Kernel Estimators in Nonparametric Regression," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    4. Chenlin Zhang & Huazhen Lin & Li Liu & Jin Liu & Yi Li, 2023. "Functional data analysis with covariate‐dependent mean and covariance structures," Biometrics, The International Biometric Society, vol. 79(3), pages 2232-2245, September.
    5. Xiong Cai & Liugen Xue & Xiaolong Pu & Xingyu Yan, 2021. "Efficient Estimation for Varying-Coefficient Mixed Effects Models with Functional Response Data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(4), pages 467-495, May.
    6. Hassan Sharghi Ghale-Joogh & S. Mohammad E. Hosseini-Nasab, 2021. "On mean derivative estimation of longitudinal and functional data: from sparse to dense," Statistical Papers, Springer, vol. 62(4), pages 2047-2066, August.

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