Skip to main content
SpringerLink
Log in

Feature Screening for Ultrahigh-dimensional Censored Data with Varying Coefficient Single-index Model

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

In this paper, we study the sure independence screening of ultrahigh-dimensional censored data with varying coefficient single-index model. This general model framework covers a large number of commonly used survival models. The property that the proposed method is not derived for a specific model is appealing in ultrahigh dimensional regressions, as it is difficult to specify a correct model for ultrahigh dimensional predictors. Once the assuming data generating process does not meet the actual one, the screening method based on the model will be problematic. We establish the sure screening property and consistency in ranking property of the proposed method. Simulations are conducted to study the finite sample performances, and the results demonstrate that the proposed method is competitive compared with the existing methods. We also illustrate the results via the analysis of data from The National Alzheimers Coordinating Center (NACC).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Fan, J., Feng, Y., Song, R. Nonparametric independence screening in sparse ultra-high-dimensional additive models. Journal of the American Statistical Association, 106: 544–557 (2011)

    Article  MathSciNet  Google Scholar 

  2. Fan, J., Lv, J. Sure independence screening for ultrahigh dimensional feature space. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70: 849–911 (2008)

    Article  MathSciNet  Google Scholar 

  3. Fan, J., Ma, Y., and Dai, W. Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Varying Coefficient Models. Journal of the American Statistical Association, 109: 1270–1284 (2014)

    Article  MathSciNet  Google Scholar 

  4. Fan, J., Song, R. Sure independence screening in generalized linear models with NP-dimensionality. The Annals of Statistics, 38: 3567–3604 (2010)

    Article  MathSciNet  Google Scholar 

  5. Gorst-Rasmussen, A., Scheike, T. Independent screening for single-index hazard rate models with ultrahigh dimensional features. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75: 217–245 (2013)

    Article  MathSciNet  Google Scholar 

  6. He, X., Wang, L., Hong, H.G. Quantile-adaptive model-free variable screening for high-dimensional heterogeneous data. The Annals of Statistics, 41: 342–369 (2013)

    Article  MathSciNet  Google Scholar 

  7. Kendall, M.G. Rank correlation methods. Griffin & Co, Lindon, 3rd ed, 1962

    Google Scholar 

  8. Li, J., Zheng, Q., Peng, L., and Huang, Z. Survival impact index and ultrahigh-dimensional model-free screening with survival outcomes. Biometrics, 72: 1145–1154 (2016)

    Article  MathSciNet  Google Scholar 

  9. Li, R., Zhong, W., Zhu, L. Feature screening via distance correlation learning. Journal of the American Statistical Association, 107: 1129–1139 (2012)

    Article  MathSciNet  Google Scholar 

  10. Lin, L., Sun, J. Adaptive conditional feature screening. Computational Statistics & Data Analysis, 94: 287–301 (2016)

    Article  MathSciNet  Google Scholar 

  11. Liu, J., Li, R., Wu, R. Feature selection for varying coefficient models with ultrahigh-dimensional covariates. Journal of the American Statistical Association, 109: 266–274 (2014)

    Article  MathSciNet  Google Scholar 

  12. Ma, S., Li, R., Tsai, C.L. Variable screening via quantile partial correlation. Journal of the American Statistical Association, 112: 650–663 (2017)

    Article  MathSciNet  Google Scholar 

  13. Mai, Q., Zou, H. The Kolmogorov filter for variable screening in high-dimensional binary classification. Biometrika, 100: 229–234 (2013)

    Article  MathSciNet  Google Scholar 

  14. Mai, Q., Zou, H. The fused Kolmogorov filter: a nonparametric model-free screening method. The Annals of Statistics, 43: 1471–1497 (2015)

    Article  MathSciNet  Google Scholar 

  15. Serfling, R.J. Approximation theorems of mathematical statistics, Vol. 162, John Wiley & Sons, Inc., New York, 2009

    Google Scholar 

  16. Song, R., Lu, W., Ma, S., Jeng, X.J. Censored rank independence screening for high-dimensional survival data. Biometrika, 101: 799–814 (2014)

    Article  MathSciNet  Google Scholar 

  17. Wang, X., Wang, Q., Zhou, X.H. A Partially varying coefficient single-index additive hazard models. Annals of the Institute of Statistical Mathematics, 67: 817–841 (2015)

    Article  MathSciNet  Google Scholar 

  18. Wied, D., Weißbach, R. Consistency of the kernel density estimator: a survey. Statistical Papers, 53: 1–21 (2012)

    Article  MathSciNet  Google Scholar 

  19. Zhao, S.D., Li, Y. Principled sure independence screening for Cox models with ultra-high-dimensional covariates. Journal of multivariate analysis, 105: 397–411 (2012)

    Article  MathSciNet  Google Scholar 

  20. Zhong, W., Zhu, L., Li, R., Cui, H. Regularized quantile regression and robust feature screening for single index models. Statistica Sinica, 26: 69–95 (2016)

    MathSciNet  MATH  Google Scholar 

  21. Zhou, T., Zhu, L. Model-free feature screening for ultrahigh dimensional censored regression. Statistics and Computing, 27: 947–961 (2017)

    Article  MathSciNet  Google Scholar 

  22. Zhu, L.P., Li, L., Li, R., Zhu, L.X. Model-free feature screening for ultrahigh-dimensional data. Journal of the American Statistical Association, 106: 1464–1475 (2011)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, China

    Yi Liu

Authors
  1. Yi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yi Liu.

Additional information

Supported by the National Natural Science Foundation of China (No.11801567).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y. Feature Screening for Ultrahigh-dimensional Censored Data with Varying Coefficient Single-index Model. Acta Math. Appl. Sin. Engl. Ser. 35, 845–861 (2019). https://doi.org/10.1007/s10255-019-0861-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-019-0861-3

Keywords

2000 MR Subject Classification

Search

Navigation