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Efficient penalized estimating method in the partially varying-coefficient single-index model

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  • Huang, Zhensheng
  • Lin, Bingqing
  • Feng, Fan
  • Pang, Zhen

Abstract

In this paper, penalized estimating equations are proposed to estimate the index parametric components, which is of primary interest, in the partially varying-coefficient single-index models (PVCSIMs). Although some procedures have been developed to estimate the index parameter in PVCSIM, the problem of how to conduct variable selection for the index in such models has not been addressed to date. To solve this problem, we propose a class of efficient penalized estimating equations, which combine the smoothly clipped absolute deviation (SCAD) penalty and a stepwise estimation method. The proposed method can simultaneously select significant variables in the index and estimate the nonzero smooth coefficient parameters. Under suitable conditions, we establish the theoretical properties of our penalized estimating procedure, including the oracle properties and the asymptotic normality for the resulting penalized estimation. We evaluate the performance of the proposed method by using Monte Carlo simulations and the application to a real dataset.

Suggested Citation

  • Huang, Zhensheng & Lin, Bingqing & Feng, Fan & Pang, Zhen, 2013. "Efficient penalized estimating method in the partially varying-coefficient single-index model," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 189-200.
    • Handle: RePEc:eee:jmvana:v:114:y:2013:i:c:p:189-200
    DOI: 10.1016/j.jmva.2012.07.011
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    References listed on IDEAS

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    1. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
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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. Pei Wang & Shunjie Chen & Sijia Yang, 2022. "Recent Advances on Penalized Regression Models for Biological Data," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    3. Ewa Strzalkowska-Kominiak & Ricardo Cao, 2014. "Beran-based approach for single-index models under censoring," Computational Statistics, Springer, vol. 29(5), pages 1243-1261, October.

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