IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v125y2014icp50-64.html
   My bibliography  Save this article

SCAD-penalized regression in additive partially linear proportional hazards models with an ultra-high-dimensional linear part

Author

Listed:
  • Lian, Heng
  • Li, Jianbo
  • Tang, Xingyu

Abstract

We consider the problem of simultaneous variable selection and estimation in additive partially linear Cox’s proportional hazards models with high-dimensional or ultra-high-dimensional covariates in the linear part. Under the sparse model assumption, we apply the smoothly clipped absolute deviation (SCAD) penalty to select the significant covariates in the linear part and use polynomial splines to estimate the nonparametric additive component functions. The oracle property of the estimator is demonstrated, in the sense that consistency in terms of variable selection can be achieved and that the nonzero coefficients are asymptotically normal with the same asymptotic variance as they would have if the zero coefficients were known a priori. Monte Carlo studies are presented to illustrate the behavior of the estimator using various tuning parameter selectors.

Suggested Citation

  • Lian, Heng & Li, Jianbo & Tang, Xingyu, 2014. "SCAD-penalized regression in additive partially linear proportional hazards models with an ultra-high-dimensional linear part," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 50-64.
    • Handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:50-64
    DOI: 10.1016/j.jmva.2013.12.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13002613
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.12.002?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. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    3. Wang, Lifeng & Li, Hongzhe & Huang, Jianhua Z., 2008. "Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1556-1569.
    4. Lan Wang & Jianhui Zhou & Annie Qu, 2012. "Penalized Generalized Estimating Equations for High-Dimensional Longitudinal Data Analysis," Biometrics, The International Biometric Society, vol. 68(2), pages 353-360, June.
    5. Simon, Noah & Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2011. "Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i05).
    6. Kim, Yongdai & Choi, Hosik & Oh, Hee-Seok, 2008. "Smoothly Clipped Absolute Deviation on High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1665-1673.
    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. Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683, June.
    9. Hu, Yuao & Lian, Heng, 2013. "Variable selection in a partially linear proportional hazards model with a diverging dimensionality," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 61-69.
    10. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
    11. Hao Helen Zhang & Wenbin Lu, 2007. "Adaptive Lasso for Cox's proportional hazards model," Biometrika, Biometrika Trust, vol. 94(3), pages 691-703.
    12. Zhu, Li-Ping & Zhu, Li-Xing, 2009. "Nonconcave penalized inverse regression in single-index models with high dimensional predictors," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 862-875, May.
    13. Zhang, Hao Helen & Cheng, Guang & Liu, Yufeng, 2011. "Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1099-1112.
    14. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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. Arfan Raheen Afzal & Jing Yang & Xuewen Lu, 2021. "Variable selection in partially linear additive hazards model with grouped covariates and a diverging number of parameters," Computational Statistics, Springer, vol. 36(2), pages 829-855, June.

    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. Hu, Yuao & Lian, Heng, 2013. "Variable selection in a partially linear proportional hazards model with a diverging dimensionality," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 61-69.
    2. Gaorong Li & Liugen Xue & Heng Lian, 2012. "SCAD-penalised generalised additive models with non-polynomial dimensionality," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 681-697.
    3. Heng Lian & Peng Lai & Hua Liang, 2013. "Partially Linear Structure Selection in Cox Models with Varying Coefficients," Biometrics, The International Biometric Society, vol. 69(2), pages 348-357, June.
    4. Heng Lian & Xin Chen & Jian-Yi Yang, 2012. "Identification of Partially Linear Structure in Additive Models with an Application to Gene Expression Prediction from Sequences," Biometrics, The International Biometric Society, vol. 68(2), pages 437-445, June.
    5. Heng Lian, 2012. "Variable selection in high-dimensional partly linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 825-839, December.
    6. Feng, Sanying & He, Wenqi & Li, Feng, 2020. "Model detection and estimation for varying coefficient panel data models with fixed effects," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    7. Lian, Heng, 2014. "Semiparametric Bayesian information criterion for model selection in ultra-high dimensional additive models," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 304-310.
    8. 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.
    9. Zhixuan Fu & Shuangge Ma & Haiqun Lin & Chirag R. Parikh & Bingqing Zhou, 2017. "Penalized Variable Selection for Multi-center Competing Risks Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 379-405, December.
    10. Guang Cheng & Hao Zhang & Zuofeng Shang, 2015. "Sparse and efficient estimation for partial spline models with increasing dimension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 93-127, February.
    11. Qu, Lianqiang & Song, Xinyuan & Sun, Liuquan, 2018. "Identification of local sparsity and variable selection for varying coefficient additive hazards models," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 119-135.
    12. Sakyajit Bhattacharya & Paul McNicholas, 2014. "A LASSO-penalized BIC for mixture model selection," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(1), pages 45-61, March.
    13. Joel L. Horowitz, 2015. "Variable selection and estimation in high-dimensional models," CeMMAP working papers 35/15, Institute for Fiscal Studies.
    14. Zhaoping Hong & Yuao Hu & Heng Lian, 2013. "Variable selection for high-dimensional varying coefficient partially linear models via nonconcave penalty," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 887-908, October.
    15. Eun Ryung Lee & Hohsuk Noh & Byeong U. Park, 2014. "Model Selection via Bayesian Information Criterion for Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 216-229, March.
    16. Joel L. Horowitz, 2015. "Variable selection and estimation in high‐dimensional models," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 48(2), pages 389-407, May.
    17. Lin, Hongmei & Lian, Heng & Liang, Hua, 2019. "Rank reduction for high-dimensional generalized additive models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 672-684.
    18. Hao, Meiling & Lin, Yunyuan & Zhao, Xingqiu, 2016. "A relative error-based approach for variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 250-262.
    19. Yanxin Wang & Qibin Fan & Li Zhu, 2018. "Variable selection and estimation using a continuous approximation to the $$L_0$$ L 0 penalty," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 191-214, February.
    20. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.

    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:jmvana:v:125:y:2014:i:c:p:50-64. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.