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Robust feature screening for ultra-high dimensional right censored data via distance correlation

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  • Chen, Xiaolin
  • Chen, Xiaojing
  • Wang, Hong

Abstract

Ultra-high dimensional data with right censored survival times are frequently collected in large-scale biomedical studies, for which feature screening has become an indispensable statistical tool. In this paper, we propose two new feature screening procedures based on distance correlation. The first approach performs feature screening through replacing the response and covariate by their cumulative distribution functions’ Kaplan–Meier estimator and empirical distribution function respectively, while the second one modifies the distance correlation via an idea of composite quantile regression. The sure screening properties are established under some rather mild technical assumptions, which allow that the dimensionality increases at an exponential rate of the sample size. The proposed methods have three desirable characteristics. Firstly, they are model-free and thus robust to model misspecification. Secondly, they behave reliably when some features contain outliers or follow heavy-tailed distributions. Thirdly, our procedures have better convergence rate than that of distance correlation screening in Li et al. (2012b). Both simulated and real examples show that the proposed methods perform competitively.

Suggested Citation

  • Chen, Xiaolin & Chen, Xiaojing & Wang, Hong, 2018. "Robust feature screening for ultra-high dimensional right censored data via distance correlation," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 118-138.
    • Handle: RePEc:eee:csdana:v:119:y:2018:i:c:p:118-138
    DOI: 10.1016/j.csda.2017.10.004
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    References listed on IDEAS

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    Cited by:

    1. Li-Pang Chen, 2021. "Feature screening based on distance correlation for ultrahigh-dimensional censored data with covariate measurement error," Computational Statistics, Springer, vol. 36(2), pages 857-884, June.
    2. Chen, Xiaolin & Zhang, Yahui & Liu, Yi & Chen, Xiaojing, 2020. "Model-free feature screening for ultra-high dimensional competing risks data," Statistics & Probability Letters, Elsevier, vol. 164(C).
    3. Xiaolin Chen & Catherine Chunling Liu & Sheng Xu, 2021. "An efficient algorithm for joint feature screening in ultrahigh-dimensional Cox’s model," Computational Statistics, Springer, vol. 36(2), pages 885-910, June.
    4. Dominic Edelmann & Thomas Welchowski & Axel Benner, 2022. "A consistent version of distance covariance for right‐censored survival data and its application in hypothesis testing," Biometrics, The International Biometric Society, vol. 78(3), pages 867-879, September.
    5. Jing Zhang & Qihua Wang & Xuan Wang, 2022. "Surrogate-variable-based model-free feature screening for survival data under the general censoring mechanism," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 379-397, April.
    6. Zhong, Wei & Wang, Jiping & Chen, Xiaolin, 2021. "Censored mean variance sure independence screening for ultrahigh dimensional survival data," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    7. Lu, Shuiyun & Chen, Xiaolin & Xu, Sheng & Liu, Chunling, 2020. "Joint model-free feature screening for ultra-high dimensional semi-competing risks data," Computational Statistics & Data Analysis, Elsevier, vol. 147(C).
    8. Chen, Xiaolin & Zhang, Yahui & Chen, Xiaojing & Liu, Yi, 2019. "A simple model-free survival conditional feature screening," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 156-160.
    9. Xiaolin Chen & Yi Liu & Qihua Wang, 2019. "Joint feature screening for ultra-high-dimensional sparse additive hazards model by the sparsity-restricted pseudo-score estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1007-1031, October.

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