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Variable selection for partially varying coefficient single-index model

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  • Sanying Feng
  • Liugen Xue

Abstract

In this paper, we consider the problem of variable selection for partially varying coefficient single-index model, and present a regularized variable selection procedure by combining basis function approximations with smoothly clipped absolute deviation penalty. The proposed procedure simultaneously selects significant variables in the single-index parametric components and the nonparametric coefficient function components. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. Finite sample performance of the proposed method is illustrated by a simulation study and real data analysis.

Suggested Citation

  • Sanying Feng & Liugen Xue, 2013. "Variable selection for partially varying coefficient single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2637-2652, December.
    • Handle: RePEc:taf:japsta:v:40:y:2013:i:12:p:2637-2652
    DOI: 10.1080/02664763.2013.823919
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    References listed on IDEAS

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    1. Wang, Lifeng & Li, Hongzhe & Huang, Jianhua Z., 2008. "Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1556-1569.
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    4. 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.
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    6. Wong, Heung & Ip, Wai-cheung & Zhang, Riquan, 2008. "Varying-coefficient single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1458-1476, January.
    7. Wang, Qihua & Xue, Liugen, 2011. "Statistical inference in partially-varying-coefficient single-index model," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 1-19, January.
    8. Zhao, Peixin & Xue, Liugen, 2010. "Variable selection for semiparametric varying coefficient partially linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1872-1883, September.
    9. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
    10. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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    Cited by:

    1. Zhensheng Huang & Xing Sun & Riquan Zhang, 2022. "Estimation for partially varying-coefficient single-index models with distorted measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 175-201, February.
    2. Zou, Yuye & Wu, Chengxin, 2023. "Composite quantile regression analysis of survival data with missing cause-of-failure information and its application to breast cancer clinical trial," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    3. Yunquan Song & Yaqi Liu & Hang Su, 2022. "Robust Variable Selection for Single-Index Varying-Coefficient Model with Missing Data in Covariates," Mathematics, MDPI, vol. 10(12), pages 1-14, June.
    4. Ping Yu & Jiang Du & Zhongzhan Zhang, 2020. "Single-index partially functional linear regression model," Statistical Papers, Springer, vol. 61(3), pages 1107-1123, June.

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