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Unified inference for sparse and dense longitudinal models

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  • Seonjin Kim
  • Zhibiao Zhao

Abstract

In longitudinal data analysis, statistical inference for sparse data and dense data could be substantially different. For kernel smoothing, the estimate of the mean function, the convergence rates and the limiting variance functions are different in the two scenarios. This phenomenon poses challenges for statistical inference, as a subjective choice between the sparse and dense cases may lead to wrong conclusions. We develop methods based on self-normalization that can adapt to the sparse and dense cases in a unified framework. Simulations show that the proposed methods outperform some existing methods. Copyright 2013, Oxford University Press.

Suggested Citation

  • Seonjin Kim & Zhibiao Zhao, 2013. "Unified inference for sparse and dense longitudinal models," Biometrika, Biometrika Trust, vol. 100(1), pages 203-212.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:1:p:203-212
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    File URL: http://hdl.handle.net/10.1093/biomet/ass050
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    Cited by:

    1. Cui, Xia & Zhao, Weihua & Lian, Heng & Liang, Hua, 2019. "Pursuit of dynamic structure in quantile additive models with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 42-60.
    2. Kim, Seonjin & Zhao, Zhibiao & Shao, Xiaofeng, 2015. "Nonparametric functional central limit theorem for time series regression with application to self-normalized confidence interval," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 277-290.
    3. 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.
    4. Jia Chen & Degui Li & Hua Liang & Suojin Wang, 2014. "Semiparametric GEE Analysis in Partially Linear Single-Index Models for Longitudinal Data," Discussion Papers 14/26, Department of Economics, University of York.
    5. Qian Huang & Jinhong You & Liwen Zhang, 2022. "Efficient inference of longitudinal/functional data models with time‐varying additive structure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 744-771, June.
    6. Yixin Chen & Weixin Yao, 2017. "Unified Inference for Sparse and Dense Longitudinal Data in Time-varying Coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 268-284, March.

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