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Feature screening in ultrahigh-dimensional partially linear models with missing responses at random

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  • Tang, Niansheng
  • Xia, Linli
  • Yan, Xiaodong

Abstract

This paper proposes a new feature screening procedure in ultrahigh-dimensional partially linear models with missing responses at random for longitudinal data based on the profile marginal kernel-assisted estimating equations imputation technique. The proposed feature screening procedure has three key merits. First, it is computationally efficient, and can be used to screen significant covariates in the presence of missing responses. Second, it does not require estimating respondent probability and is robust to the misspecification of respondent probability models. Third, the univariate kernel smoothing method is adopted to estimate nonparametric functions, and is employed to impute estimating equations with missing responses at random, which avoids the well-known “curse of dimensionality”. The ranking consistency property and the sure screening property are shown under some regularity conditions. Simulation studies are conducted to investigate the finite sample performance of the proposed screening procedure. An example is used to illustrate the proposed procedure.

Suggested Citation

  • Tang, Niansheng & Xia, Linli & Yan, Xiaodong, 2019. "Feature screening in ultrahigh-dimensional partially linear models with missing responses at random," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 208-227.
    • Handle: RePEc:eee:csdana:v:133:y:2019:i:c:p:208-227
    DOI: 10.1016/j.csda.2018.10.003
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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. Qihua Wang & Yongjin Li, 2018. "How to Make Model†free Feature Screening Approaches for Full Data Applicable to the Case of Missing Response?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(2), pages 324-346, June.
    3. Ibrahim, Joseph G. & Zhu, Hongtu & Tang, Niansheng, 2008. "Model Selection Criteria for Missing-Data Problems Using the EM Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1648-1658.
    4. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    5. 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.
    6. Hengjian Cui & Runze Li & Wei Zhong, 2015. "Model-Free Feature Screening for Ultrahigh Dimensional Discriminant Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 630-641, June.
    7. 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.
    8. 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.
    9. 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.
    10. Zhong‐Yi Zhu & Xuming He & Wing‐Kam Fung, 2003. "Local Influence Analysis for Penalized Gaussian Likelihood Estimators in Partially Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 767-780, December.
    11. Lai, Peng & Liu, Yiming & Liu, Zhi & Wan, Yi, 2017. "Model free feature screening for ultrahigh dimensional data with responses missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 201-216.
    12. Peirong Xu & Lixing Zhu & Yi Li, 2014. "Ultrahigh dimensional time course feature selection," Biometrics, The International Biometric Society, vol. 70(2), pages 356-365, June.
    13. Tang, Niansheng & Yan, Xiaodong & Zhao, Puying, 2018. "Exponentially tilted likelihood inference on growing dimensional unconditional moment models," Journal of Econometrics, Elsevier, vol. 202(1), pages 57-74.
    14. Yanyuan Ma & Jeng-Min Chiou & Naisyin Wang, 2006. "Efficient semiparametric estimator for heteroscedastic partially linear models," Biometrika, Biometrika Trust, vol. 93(1), pages 75-84, March.
    15. Zhou, Yong & Wan, Alan T. K & Wang, Xiaojing, 2008. "Estimating Equations Inference With Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1187-1199.
    16. 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.
    17. Sihai Dave Zhao & Yi Li, 2014. "Score test variable screening," Biometrics, The International Biometric Society, vol. 70(4), pages 862-871, December.
    18. Zhang, Jing & Liu, Yanyan & Wu, Yuanshan, 2017. "Correlation rank screening for ultrahigh-dimensional survival data," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 121-132.
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