IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v170y2022ics016794732200010x.html
   My bibliography  Save this article

ℓ0-Regularized high-dimensional accelerated failure time model

Author

Listed:
  • Cheng, Chao
  • Feng, Xingdong
  • Huang, Jian
  • Jiao, Yuling
  • Zhang, Shuang

Abstract

We develop a constructive approach for ℓ0-penalized estimation in the sparse accelerated failure time (AFT) model with high-dimensional covariates. The proposed approach is based on Stute's weighted least squares criterion combined with ℓ0-penalization. This method is a computational algorithm that generates a sequence of solutions iteratively, based on active sets derived from primal and dual information and root finding according to the Karush-Kuhn-Tucker (KKT) conditions. We refer to the proposed method as AFT-SDAR (for support detection and root finding). An important aspect of our theoretical results is that we directly concern the sequence of solutions generated based on the AFT-SDAR algorithm. We prove that the estimation errors of the solution sequence decay exponentially to the optimal error bound with high probability, as long as the covariate matrix satisfies a mild regularity condition which is necessary and sufficient for model identification even in the setting of high-dimensional linear regression. An adaptive version of AFT-SDAR is also proposed, i.e., AFT-ASDAR, which determines the support size of the estimated coefficient in a data-driven fashion. Simulation studies demonstrate the superior performance of the proposed method over the lasso and MCP in terms of accuracy and speed. The application of the proposed method is also illustrated by analyzing a real data set.

Suggested Citation

  • Cheng, Chao & Feng, Xingdong & Huang, Jian & Jiao, Yuling & Zhang, Shuang, 2022. "ℓ0-Regularized high-dimensional accelerated failure time model," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:csdana:v:170:y:2022:i:c:s016794732200010x
    DOI: 10.1016/j.csda.2022.107430
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016794732200010X
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2022.107430?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Hu, Jianwei & Chai, Hao, 2013. "Adjusted regularized estimation in the accelerated failure time model with high dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 96-114.
    3. Johnson, Brent A. & Lin, D.Y. & Zeng, Donglin, 2008. "Penalized Estimating Functions and Variable Selection in Semiparametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 672-680, June.
    4. Brent A. Johnson, 2008. "Variable selection in semiparametric linear regression with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 351-370, April.
    5. 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.
    6. Jian Huang & Shuangge Ma & Huiliang Xie, 2006. "Regularized Estimation in the Accelerated Failure Time Model with High-Dimensional Covariates," Biometrics, The International Biometric Society, vol. 62(3), pages 813-820, September.
    7. 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.
    8. T. Cai & J. Huang & L. Tian, 2009. "Regularized Estimation for the Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 65(2), pages 394-404, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Zhihua Sun & Yi Liu & Kani Chen & Gang Li, 2022. "Broken adaptive ridge regression for right-censored survival data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 69-91, February.
    3. Hu, Jianwei & Chai, Hao, 2013. "Adjusted regularized estimation in the accelerated failure time model with high dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 96-114.
    4. Xingwei Tong & Xin He & Liuquan Sun & Jianguo Sun, 2009. "Variable Selection for Panel Count Data via Non‐Concave Penalized Estimating Function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 620-635, December.
    5. Yan, Xiaodong & Wang, Hongni & Wang, Wei & Xie, Jinhan & Ren, Yanyan & Wang, Xinjun, 2021. "Optimal model averaging forecasting in high-dimensional survival analysis," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1147-1155.
    6. Guo-Liang Tian & Mingqiu Wang & Lixin Song, 2014. "Variable selection in the high-dimensional continuous generalized linear model with current status data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(3), pages 467-483, March.
    7. Dong, Qingkai & Liu, Binxia & Zhao, Hui, 2023. "Weighted least squares model averaging for accelerated failure time models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    8. Wang Zhu & Wang C.Y., 2010. "Buckley-James Boosting for Survival Analysis with High-Dimensional Biomarker Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-33, June.
    9. Shan Luo & Zehua Chen, 2014. "Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1229-1240, September.
    10. Shi Chen & Wolfgang Karl Hardle & Brenda L'opez Cabrera, 2020. "Regularization Approach for Network Modeling of German Power Derivative Market," Papers 2009.09739, arXiv.org.
    11. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    12. Peter Bühlmann & Jacopo Mandozzi, 2014. "High-dimensional variable screening and bias in subsequent inference, with an empirical comparison," Computational Statistics, Springer, vol. 29(3), pages 407-430, June.
    13. Anders Bredahl Kock, 2012. "On the Oracle Property of the Adaptive Lasso in Stationary and Nonstationary Autoregressions," CREATES Research Papers 2012-05, Department of Economics and Business Economics, Aarhus University.
    14. Tang, Yanlin & Song, Xinyuan & Wang, Huixia Judy & Zhu, Zhongyi, 2013. "Variable selection in high-dimensional quantile varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 115-132.
    15. Joseph G. Ibrahim & Hongtu Zhu & Ramon I. Garcia & Ruixin Guo, 2011. "Fixed and Random Effects Selection in Mixed Effects Models," Biometrics, The International Biometric Society, vol. 67(2), pages 495-503, June.
    16. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    17. Li, Xinyi & Wang, Li & Nettleton, Dan, 2019. "Sparse model identification and learning for ultra-high-dimensional additive partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 204-228.
    18. 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.
    19. Jianqing Fan & Yang Feng & Jiancheng Jiang & Xin Tong, 2016. "Feature Augmentation via Nonparametrics and Selection (FANS) in High-Dimensional Classification," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 275-287, March.
    20. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:170:y:2022:i:c:s016794732200010x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.