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Efficient semiparametric regression for longitudinal data with nonparametric covariance estimation

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  • Yehua Li

Abstract

For longitudinal data, when the within-subject covariance is misspecified, the semiparametric regression estimator may be inefficient. We propose a method that combines the efficient semiparametric estimator with nonparametric covariance estimation, and is robust against misspecification of covariance models. We show that kernel covariance estimation provides uniformly consistent estimators for the within-subject covariance matrices, and the semiparametric profile estimator with substituted nonparametric covariance is still semiparametrically efficient. The finite sample performance of the proposed estimator is illustrated by simulation. In an application to CD4 count data from an AIDS clinical trial, we extend the proposed method to a functional analysis of the covariance model. Copyright 2011, Oxford University Press.

Suggested Citation

  • Yehua Li, 2011. "Efficient semiparametric regression for longitudinal data with nonparametric covariance estimation," Biometrika, Biometrika Trust, vol. 98(2), pages 355-370.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:2:p:355-370
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    Cited by:

    1. Zhang, Xin & Wang, Chong & Wu, Yichao, 2018. "Functional envelope for model-free sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 37-50.
    2. Liu, Shu & You, Jinhong & Lian, Heng, 2017. "Estimation and model identification of longitudinal data time-varying nonparametric models," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 116-136.
    3. 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).
    4. Zheng, Xueying & Xue, Lan & Qu, Annie, 2018. "Time-varying correlation structure estimation and local-feature detection for spatio-temporal data," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 221-239.
    5. 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).
    6. Christopher Withers & Saralees Nadarajah, 2014. "Non-parametric confidence intervals for covariance and correlation," METRON, Springer;Sapienza Università di Roma, vol. 72(3), pages 283-306, October.
    7. Cho, Hyunkeun & Kim, Seonjin, 2017. "Model specification test in a semiparametric regression model for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 105-116.
    8. Jia Chen & Degui Li & Yingcun Xia, 2015. "New Semiparametric Estimation Procedure for Functional Coefficient Longitudinal Data Models," Discussion Papers 15/17, Department of Economics, University of York.
    9. Huang, Chao & Farewell, Daniel & Pan, Jianxin, 2017. "A calibration method for non-positive definite covariance matrix in multivariate data analysis," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 45-52.
    10. Jing Lv & Chaohui Guo, 2019. "Quantile estimations via modified Cholesky decomposition for longitudinal single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1163-1199, October.
    11. Weicheng Zhu & Sheng Xu & Catherine C. Liu & Yehua Li, 2023. "Minimax powerful functional analysis of covariance tests with application to longitudinal genome‐wide association studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 266-295, March.
    12. Peirong Xu & Jun Zhang & Xingfang Huang & Tao Wang, 2016. "Efficient estimation for marginal generalized partially linear single-index models with longitudinal data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 413-431, September.
    13. Jing Lv & Chaohui Guo & Jibo Wu, 2019. "Smoothed empirical likelihood inference via the modified Cholesky decomposition for quantile varying coefficient models with longitudinal data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 999-1032, September.
    14. Yuichi Goto & Koichi Arakaki & Yan Liu & Masanobu Taniguchi, 2023. "Homogeneity tests for one-way models with dependent errors under correlated groups," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 163-183, March.
    15. Chen, Jia & Li, Degui & Xia, Yingcun, 2019. "Estimation of a rank-reduced functional-coefficient panel data model with serial correlation," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 456-479.
    16. Rui Li & Chenlei Leng & Jinhong You, 2017. "A Semiparametric Regression Model for Longitudinal Data with Non-stationary Errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 932-950, December.

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