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A Flexibly Conditional Screening Approach via a Nonparametric Quantile Partial Correlation

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  • Xiaochao Xia

    (College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
    These authors contributed equally to this work.)

  • Hao Ming

    (College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
    These authors contributed equally to this work.)

Abstract

Considering the influence of conditional variables is crucial to statistical modeling, ignoring this may lead to misleading results. Recently, Ma, Li and Tsai proposed the quantile partial correlation (QPC)-based screening approach that takes into account conditional variables for ultrahigh dimensional data. In this paper, we propose a nonparametric version of quantile partial correlation (NQPC), which is able to describe the influence of conditional variables on other relevant variables more flexibly and precisely. Specifically, the NQPC firstly removes the effect of conditional variables via fitting two nonparametric additive models, which differs from the conventional partial correlation that fits two parametric models, and secondly computes the QPC of the resulting residuals as NQPC. This measure is very useful in the situation where the conditional variables are highly nonlinearly correlated with both the predictors and response. Then, we employ this NQPC as the screening utility to do variable screening. A variable screening procedure based on NPQC (NQPC-SIS) is proposed. Theoretically, we prove that the NQPC-SIS enjoys the sure screening property that, with probability going to one, the selected subset can recruit all the truly important predictors under mild conditions. Finally, extensive simulations and an empirical application are carried out to demonstrate the usefulness of our proposal.

Suggested Citation

  • Xiaochao Xia & Hao Ming, 2022. "A Flexibly Conditional Screening Approach via a Nonparametric Quantile Partial Correlation," Mathematics, MDPI, vol. 10(24), pages 1-32, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4638-:d:996471
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    References listed on IDEAS

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    1. Yi Liu & Qihua Wang, 2018. "Model-free feature screening for ultrahigh-dimensional data conditional on some variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 283-301, April.
    2. 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.
    3. Emre Barut & Jianqing Fan & Anneleen Verhasselt, 2016. "Conditional Sure Independence Screening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1266-1277, July.
    4. Jialiang Li & Qi Zheng & Limin Peng & Zhipeng Huang, 2016. "Survival impact index and ultrahigh‐dimensional model‐free screening with survival outcomes," Biometrics, The International Biometric Society, vol. 72(4), pages 1145-1154, December.
    5. Zhao Chen & Jianqing Fan & Runze Li, 2018. "Error Variance Estimation in Ultrahigh-Dimensional Additive Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 315-327, January.
    6. Xiaochao Xia & Binyan Jiang & Jialiang Li & Wenyang Zhang, 2016. "Low-dimensional confounder adjustment and high-dimensional penalized estimation for survival analysis," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 547-569, October.
    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. 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.
    9. Guodong Li & Yang Li & Chih-Ling Tsai, 2015. "Quantile Correlations and Quantile Autoregressive Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 246-261, March.
    10. 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.
    11. Tingyou Zhou & Liping Zhu & Chen Xu & Runze Li, 2020. "Model-Free Forward Screening Via Cumulative Divergence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1393-1405, July.
    12. Shujie Ma & Runze Li & Chih-Ling Tsai, 2017. "Variable Screening via Quantile Partial Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 650-663, April.
    13. 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.
    14. 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.
    15. Wanjun Liu & Yuan Ke & Jingyuan Liu & Runze Li, 2022. "Model-Free Feature Screening and FDR Control With Knockoff Features," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 428-443, January.
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