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Time-Varying Additive Models for Longitudinal Data

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  • Xiaoke Zhang
  • Byeong U. Park
  • Jane-ling Wang

Abstract

The additive model is an effective dimension-reduction approach that also provides flexibility in modeling the relation between a response variable and key covariates. The literature is largely developed to scalar response and vector covariates. In this article, more complex data are of interest, where both the response and the covariates are functions. We propose a functional additive model together with a new backfitting algorithm to estimate the unknown regression functions, whose components are time-dependent additive functions of the covariates. Such functional data may not be completely observed since measurements may only be collected intermittently at discrete time points. We develop a unified platform and an efficient approach that can cover both dense and sparse functional data and the needed theory for statistical inference. We also establish the oracle properties of the proposed estimators of the component functions.

Suggested Citation

  • Xiaoke Zhang & Byeong U. Park & Jane-ling Wang, 2013. "Time-Varying Additive Models for Longitudinal Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 983-998, September.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:503:p:983-998
    DOI: 10.1080/01621459.2013.778776
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    Citations

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    Cited by:

    1. 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.
    2. Zhang, Xiaoke & Zhong, Qixian & Wang, Jane-Ling, 2020. "A new approach to varying-coefficient additive models with longitudinal covariates," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    3. Lee, Kyeongeun & Lee, Young K. & Park, Byeong U. & Yang, Seong J., 2018. "Time-dynamic varying coefficient models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 50-65.
    4. Yang, Seong J. & Park, Byeong U., 2014. "Efficient estimation for partially linear varying coefficient models when coefficient functions have different smoothing variables," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 100-113.
    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. Zhao, Weihua & Zhou, Yan & Lian, Heng, 2018. "Time-varying quantile single-index model for multivariate responses," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 32-49.
    7. Mammen, Enno & Martínez Miranda, María Dolores & Nielsen, Jens Perch, 2015. "In-sample forecasting applied to reserving and mesothelioma mortality," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 76-86.
    8. 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.

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