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On a Principal Varying Coefficient Model

Author

Listed:
  • Qian Jiang
  • Hansheng Wang
  • Yingcun Xia
  • Guohua Jiang

Abstract

We propose a novel varying coefficient model (VCM), called principal varying coefficient model (PVCM), by characterizing the varying coefficients through linear combinations of a few principal functions. Compared with the conventional VCM, PVCM reduces the actual number of nonparametric functions and thus has better estimation efficiency. Compared with the semivarying coefficient model (SVCM), PVCM is more flexible but with the same estimation efficiency when the number of principal functions in PVCM and the number of varying coefficients in SVCM are the same. Model estimation and identification are investigated, and the better estimation efficiency is justified theoretically. Incorporating the estimation with the L 1 penalty, variables in the linear combinations can be selected automatically, and hence, the estimation efficiency can be further improved. Numerical experiments suggest that the model together with the estimation method is useful even when the number of covariates is large. Supplementary materials for this article are available online.

Suggested Citation

  • Qian Jiang & Hansheng Wang & Yingcun Xia & Guohua Jiang, 2013. "On a Principal Varying Coefficient Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 228-236, March.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:501:p:228-236
    DOI: 10.1080/01621459.2012.736904
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    References listed on IDEAS

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    1. Wang, Hansheng & Xia, Yingcun, 2008. "Sliced Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 811-821, June.
    2. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    3. Fan, Jianqing & Jiang, Jiancheng, 2005. "Nonparametric Inferences for Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 890-907, September.
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    Cited by:

    1. Zhao, Weihua & Jiang, Xuejun & Lian, Heng, 2018. "A principal varying-coefficient model for quantile regression: Joint variable selection and dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 269-280.
    2. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Chen, Jia & Li, Degui & Xia, Yingcun, 2019. "Estimation of a rank-reduced functional-coefficient panel data model with serial correlation," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 456-479.

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