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Feature Selection for Varying Coefficient Models With Ultrahigh-Dimensional Covariates

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  • Jingyuan Liu
  • Runze Li
  • Rongling Wu

Abstract

This article is concerned with feature screening and variable selection for varying coefficient models with ultrahigh-dimensional covariates. We propose a new feature screening procedure for these models based on conditional correlation coefficient. We systematically study the theoretical properties of the proposed procedure, and establish their sure screening property and the ranking consistency. To enhance the finite sample performance of the proposed procedure, we further develop an iterative feature screening procedure. Monte Carlo simulation studies were conducted to examine the performance of the proposed procedures. In practice, we advocate a two-stage approach for varying coefficient models. The two-stage approach consists of (a) reducing the ultrahigh dimensionality by using the proposed procedure and (b) applying regularization methods for dimension-reduced varying coefficient models to make statistical inferences on the coefficient functions. We illustrate the proposed two-stage approach by a real data example. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:505:p:266-274
    DOI: 10.1080/01621459.2013.850086
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    4. Runze Li & Wei Zhong & Liping Zhu, 2012. "Feature Screening via Distance Correlation Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1129-1139, September.
    5. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    6. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    7. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
    8. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
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