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Simultaneous selection and inference for varying coefficients with zero regions: a soft‐thresholding approach

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  • Yuan Yang
  • Ziyang Pan
  • Jian Kang
  • Chad Brummett
  • Yi Li

Abstract

Varying coefficient models have been used to explore dynamic effects in many scientific areas, such as in medicine, finance, and epidemiology. As most existing models ignore the existence of zero regions, we propose a new soft‐thresholded varying coefficient model, where the coefficient functions are piecewise smooth with zero regions. Our new modeling approach enables us to perform variable selection, detect the zero regions of selected variables, obtain point estimates of the varying coefficients with zero regions, and construct a new type of sparse confidence intervals that accommodate zero regions. We prove the asymptotic properties of the estimator, based on which we draw statistical inference. Our simulation study reveals that the proposed sparse confidence intervals achieve the desired coverage probability. We apply the proposed method to analyze a large‐scale preoperative opioid study.

Suggested Citation

  • Yuan Yang & Ziyang Pan & Jian Kang & Chad Brummett & Yi Li, 2023. "Simultaneous selection and inference for varying coefficients with zero regions: a soft‐thresholding approach," Biometrics, The International Biometric Society, vol. 79(4), pages 3388-3401, December.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:4:p:3388-3401
    DOI: 10.1111/biom.13900
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    References listed on IDEAS

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    1. Jingyuan Liu & Runze Li & Rongling Wu, 2014. "Feature Selection for Varying Coefficient Models With Ultrahigh-Dimensional Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 266-274, March.
    2. Colin Wu & Kai Yu & Chin-Tsang Chiang, 2000. "A Two-Step Smoothing Method for Varying-Coefficient Models with Repeated Measurements," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 519-543, September.
    3. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    4. R. L. Eubank & Chunfeng Huang & Y. Muñoz Maldonado & Naisyin Wang & Suojin Wang & R. J. Buchanan, 2004. "Smoothing spline estimation in varying‐coefficient models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 653-667, August.
    5. Kejun He & Heng Lian & Shujie Ma & Jianhua Z. Huang, 2018. "Dimensionality Reduction and Variable Selection in Multivariate Varying-Coefficient Models With a Large Number of Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 746-754, April.
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