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Unified Variable Selection for Varying Coefficient Models with Longitudinal Data

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Abstract

Variable selection for varying coefficient models includes the separation of varying and constant effects, and the selection of variables with nonzero varying effects and those with nonzero constant effects. This paper proposes a unified variable selection approach called the double-penalized quadratic inference functions method for varying coefficient models of longitudinal data. The proposed method can not only separate varying coefficients and constant coefficients, but also estimate and select the nonzero varying coefficients and nonzero constant coefficients. It is suitable for variable selection of linear models, varying coefficient models, and partial linear varying coefficient models. Under regularity conditions, the proposed method is consistent in both separation and selection of varying coefficients and constant coefficients. The obtained estimators of varying coefficients possess the optimal convergence rate of non-parametric function estimation, and the estimators of nonzero constant coefficients are consistent and asymptotically normal. Finally, the authors investigate the finite sample performance of the proposed method through simulation studies and a real data analysis. The results show that the proposed method performs better than the existing competitor.

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Authors and Affiliations

  1. School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu, 233000, China

    Xiaoli Xu

  2. College of Mathematics and Statistics, Institute of Statistical Sciences, Shenzhen Key Laboratory of Advanced Machine Learning and Applications, Shenzhen University, Shenzhen, 518061, China

    Yan Zhou

  3. Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, 233000, China

    Kongsheng Zhang & Mingtao Zhao

Authors
  1. Xiaoli Xu
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  2. Yan Zhou
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  3. Kongsheng Zhang
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  4. Mingtao Zhao
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Corresponding author

Correspondence to Mingtao Zhao.

Additional information

This paper was supported in part by the National Science Foundation of China under Grant Nos. 12071305 and 71803001, in part by the national social science foundation of China under Grant No. 19BTJ014, in part by the University Social Science Research Project of Anhui Province under Grant No. SK2020A0051, and in part by the Social Science Foundation of the Ministry of Education of China under Grant Nos. 19YJCZH250 and 21YJAZH081.

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Xu, X., Zhou, Y., Zhang, K. et al. Unified Variable Selection for Varying Coefficient Models with Longitudinal Data. J Syst Sci Complex 36, 822–842 (2023). https://doi.org/10.1007/s11424-022-2109-1

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  • DOI: https://doi.org/10.1007/s11424-022-2109-1

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