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Semiparametric Time‐Varying Coefficients Regression Model for Longitudinal Data

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  • YANQING SUN
  • HULIN WU

Abstract

. In this paper, we consider a semiparametric time‐varying coefficients regression model where the influences of some covariates vary non‐parametrically with time while the effects of the remaining covariates follow certain parametric functions of time. The weighted least squares type estimators for the unknown parameters of the parametric coefficient functions as well as the estimators for the non‐parametric coefficient functions are developed. We show that the kernel smoothing that avoids modelling of the sampling times is asymptotically more efficient than a single nearest neighbour smoothing that depends on the estimation of the sampling model. The asymptotic optimal bandwidth is also derived. A hypothesis testing procedure is proposed to test whether some covariate effects follow certain parametric forms. Simulation studies are conducted to compare the finite sample performances of the kernel neighbourhood smoothing and the single nearest neighbour smoothing and to check the empirical sizes and powers of the proposed testing procedures. An application to a data set from an AIDS clinical trial study is provided for illustration.

Suggested Citation

  • Yanqing Sun & Hulin Wu, 2005. "Semiparametric Time‐Varying Coefficients Regression Model for Longitudinal Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(1), pages 21-47, March.
    • Handle: RePEc:bla:scjsta:v:32:y:2005:i:1:p:21-47
    DOI: 10.1111/j.1467-9469.2005.00413.x
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    Cited by:

    1. Chen, Xuerong & Tang, Niansheng & Zhou, Yong, 2016. "Quantile regression of longitudinal data with informative observation times," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 176-188.
    2. 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.
    3. Sun, Yanqing & Li, Mei & Gilbert, Peter B., 2016. "Goodness-of-fit test of the stratified mark-specific proportional hazards model with continuous mark," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 348-358.
    4. Fei Heng & Yanqing Sun & Seunggeun Hyun & Peter B. Gilbert, 2020. "Analysis of the time-varying Cox model for the cause-specific hazard functions with missing causes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 731-760, October.
    5. Yan Li & Liangjun Su & Yuewu Xu, 2015. "A Combined Approach to the Inference of Conditional Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 203-220, April.
    6. Yanqing Sun & Rajeshwari Sundaram & Yichuan Zhao, 2009. "Empirical Likelihood Inference for the Cox Model with Time‐dependent Coefficients via Local Partial Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 444-462, September.
    7. Qu, Lianqiang & Song, Xinyuan & Sun, Liuquan, 2018. "Identification of local sparsity and variable selection for varying coefficient additive hazards models," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 119-135.
    8. Peixin Zhao & Liugen Xue, 2012. "Variable selection in semiparametric regression analysis for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 213-231, February.

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