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Composite Quantile Estimation for Kink Model with Longitudinal Data

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Abstract

Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point. In quantile regression for longitudinal data, kink point where the kink effect happens is often assumed to be heterogeneous across different quantiles. However, the kink point tends to be the same across different quantiles, especially in a region of neighboring quantile levels. Incorporating such homogeneity information could increase the estimation efficiency of the common kink point. In this paper, we propose a composite quantile estimation approach for the common kink point by combining information from multiple neighboring quantiles. Asymptotic normality of the proposed estimator is studied. In addition, we also develop a sup-likelihood-ratio test to check the existence of the kink effect at a given quantile level. A test-inversion confidence interval for the common kink point is also developed based on the quantile rank score test. The simulation studies show that the proposed composite kink estimator is more efficient than the single quantile regression estimator. We also illustrate the proposed method via an application to a longitudinal data set on blood pressure and body mass index.

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Acknowledgements

We thank the Editor, the Associate Editor and three referees for their encouragements and insightful comments which have substantially improved the paper.

Author information

Authors and Affiliations

  1. School of Statistics and Data Science, Nankai University, Tian**, 300071, P. R. China

    Chuang Wan

  2. MOE Key Lab of Econometrics, WISE, Department of Statistics and Data Science, School of Economics, **amen University, **amen, 361000, P. R. China

    Wei Zhong & Ying Fang

Authors
  1. Chuang Wan
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  2. Wei Zhong
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  3. Ying Fang
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Corresponding author

Correspondence to Wei Zhong.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 11922117, 11771361) and Fujian Provincial Science Fund for Distinguished Young Scholars (Grant No. 2019J06004)

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Wan, C., Zhong, W. & Fang, Y. Composite Quantile Estimation for Kink Model with Longitudinal Data. Acta. Math. Sin.-English Ser. 39, 412–438 (2023). https://doi.org/10.1007/s10114-023-1557-4

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  • DOI: https://doi.org/10.1007/s10114-023-1557-4

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