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Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data

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  • Lai, Peng
  • Wang, Qihua
  • Lian, Heng

Abstract

In this paper, we present an estimation approach based on generalized estimating equations and a variable selection procedure for single-index models when the observed data are clustered. Unlike the case of independent observations, bias-correction is necessary when general working correlation matrices are used in the estimating equations. Our variable selection procedure based on smooth-threshold estimating equations (Ueki (2009) [23]) can automatically eliminate irrelevant parameters by setting them as zeros and is computationally simpler than alternative approaches based on shrinkage penalty. The resulting estimator consistently identifies the significant variables in the index, even when the working correlation matrix is misspecified. The asymptotic property of the estimator is the same whether or not the nonzero parameters are known (in both cases we use the same estimating equations), thus achieving the oracle property in the sense of Fan and Li (2001) [10]. The finite sample properties of the estimator are illustrated by some simulation examples, as well as a real data application.

Suggested Citation

  • Lai, Peng & Wang, Qihua & Lian, Heng, 2012. "Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 422-432.
  • Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:422-432
    DOI: 10.1016/j.jmva.2011.08.009
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    References listed on IDEAS

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    10. Masao Ueki, 2009. "A note on automatic variable selection using smooth-threshold estimating equations," Biometrika, Biometrika Trust, vol. 96(4), pages 1005-1011.
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    Citations

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    Cited by:

    1. Tian, Ruiqin & Xue, Liugen & Xu, Dengke, 2016. "Automatic variable selection for varying coefficient models with longitudinal data," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 84-90.
    2. Jing Lv & Hu Yang & Chaohui Guo, 2016. "Smoothing combined generalized estimating equations in quantile partially linear additive models with longitudinal data," Computational Statistics, Springer, vol. 31(3), pages 1203-1234, September.
    3. Yang, Suigen & Xue, Liugen & Li, Gaorong, 2014. "Simultaneous confidence band for single-index random effects models with longitudinal data," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 6-14.
    4. Liu, Jicai & Zhang, Riquan & Zhao, Weihua & Lv, Yazhao, 2013. "A robust and efficient estimation method for single index models," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 226-238.
    5. repec:spr:aistmt:v:70:y:2018:i:3:d:10.1007_s10463-017-0599-8 is not listed on IDEAS
    6. Lai, Peng & Li, Gaorong & Lian, Heng, 2013. "Quadratic inference functions for partially linear single-index models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 115-127.

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