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Marginal quantile regression for varying coefficient models with longitudinal data

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Abstract

In this paper, we investigate the quantile varying coefficient model for longitudinal data, where the unknown nonparametric functions are approximated by polynomial splines and the estimators are obtained by minimizing the quadratic inference function. The theoretical properties of the resulting estimators are established, and they achieve the optimal convergence rate for the nonparametric functions. Since the objective function is non-smooth, an estimation procedure is proposed that uses induced smoothing and we prove that the smoothed estimator is asymptotically equivalent to the original estimator. Moreover, we propose a variable selection procedure based on the regularization method, which can simultaneously estimate and select important nonparametric components and has the asymptotic oracle property. Extensive simulations and a real data analysis show the usefulness of the proposed method.

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Acknowledgements

We sincerely thank the Editor/Professor Hironori Fujisawa, an associate editor and two anonymous reviewers, for their insightful comments that have led to significant improvement of the paper. Zhao’s research is supported in part by National Social Science Foundation of China (15BTJ027). Zhang’s research is supported by the National Natural Science Foundation of China Grant 11671374 and 71631006. Heng Lian’s research is partially supported by City University of Hong Kong Start-up Grant 7200521 and RGC General Research Fund 11301718.

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Correspondence to Weihua Zhao.

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Cite this article

Zhao, W., Zhang, W. & Lian, H. Marginal quantile regression for varying coefficient models with longitudinal data. Ann Inst Stat Math 72, 213–234 (2020). https://doi.org/10.1007/s10463-018-0684-7

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Keywords

  • Longitudinal data
  • Quadratic inference function
  • Quantile regression
  • Varying coefficient model