IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v41y2014i3p467-483.html
   My bibliography  Save this article

Variable selection in the high-dimensional continuous generalized linear model with current status data

Author

Listed:
  • Guo-Liang Tian
  • Mingqiu Wang
  • Lixin Song

Abstract

In survival studies, current status data are frequently encountered when some individuals in a study are not successively observed. This paper considers the problem of simultaneous variable selection and parameter estimation in the high-dimensional continuous generalized linear model with current status data. We apply the penalized likelihood procedure with the smoothly clipped absolute deviation penalty to select significant variables and estimate the corresponding regression coefficients. With a proper choice of tuning parameters, the resulting estimator is shown to be a root n / p n -consistent estimator under some mild conditions. In addition, we show that the resulting estimator has the same asymptotic distribution as the estimator obtained when the true model is known. The finite sample behavior of the proposed estimator is evaluated through simulation studies and a real example.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:3:p:467-483
    DOI: 10.1080/02664763.2013.840271
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2013.840271
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2013.840271?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. Jelena Bradic & Jianqing Fan & Weiwei Wang, 2011. "Penalized composite quasi‐likelihood for ultrahigh dimensional variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 325-349, June.
    2. 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.
    3. 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.
    4. K. F. Lam & Hongqi Xue, 2005. "A semiparametric regression cure model with current status data," Biometrika, Biometrika Trust, vol. 92(3), pages 573-586, September.
    5. Wang, Mingqiu & Song, Lixin & Wang, Xiaoguang, 2010. "Bridge estimation for generalized linear models with a diverging number of parameters," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1584-1596, November.
    6. Wang, Lianming & Lin, Xiaoyan, 2011. "A Bayesian approach for analyzing case 2 interval-censored data under the semiparametric proportional odds model," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 876-883, July.
    7. 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.
    8. Xue H. & Lam K.F. & Li G., 2004. "Sieve Maximum Likelihood Estimator for Semiparametric Regression Models With Current Status Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 346-356, January.
    9. 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.
    10. 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.
    11. 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.
    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. 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.
    2. Joel L. Horowitz, 2015. "Variable selection and estimation in high-dimensional models," CeMMAP working papers 35/15, Institute for Fiscal Studies.
    3. 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.
    4. 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.
    5. Joel L. Horowitz, 2015. "Variable selection and estimation in high-dimensional models," Canadian Journal of Economics, Canadian Economics Association, vol. 48(2), pages 389-407, May.
    6. Joel L. Horowitz, 2015. "Variable selection and estimation in high-dimensional models," CeMMAP working papers CWP35/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Fei Jin & Lung-fei Lee, 2018. "Lasso Maximum Likelihood Estimation of Parametric Models with Singular Information Matrices," Econometrics, MDPI, vol. 6(1), pages 1-24, February.
    8. 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.
    9. Dengke Xu & Zhongzhan Zhang & Liucang Wu, 2014. "Variable selection in high-dimensional double generalized linear models," Statistical Papers, Springer, vol. 55(2), pages 327-347, May.
    10. 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.
    11. Jin, Fei & Lee, Lung-fei, 2018. "Irregular N2SLS and LASSO estimation of the matrix exponential spatial specification model," Journal of Econometrics, Elsevier, vol. 206(2), pages 336-358.
    12. Zhang, Shucong & Zhou, Yong, 2018. "Variable screening for ultrahigh dimensional heterogeneous data via conditional quantile correlations," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 1-13.
    13. Abdul Wahid & Dost Muhammad Khan & Ijaz Hussain, 2017. "Robust Adaptive Lasso method for parameter’s estimation and variable selection in high-dimensional sparse models," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-17, August.
    14. Engler David & Li Yi, 2009. "Survival Analysis with High-Dimensional Covariates: An Application in Microarray Studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-24, February.
    15. Joel L. Horowitz & Lars Nesheim, 2018. "Using penalized likelihood to select parameters in a random coefficients multinomial logit model," CeMMAP working papers CWP29/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Kean Ming Tan & Lan Wang & Wen‐Xin Zhou, 2022. "High‐dimensional quantile regression: Convolution smoothing and concave regularization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 205-233, February.
    17. Hirose, Kei & Tateishi, Shohei & Konishi, Sadanori, 2013. "Tuning parameter selection in sparse regression modeling," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 28-40.
    18. 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).
    19. Weihua Zhao & Riquan Zhang & Jicai Liu, 2013. "Robust variable selection for the varying coefficient model based on composite L 1 -- L 2 regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 2024-2040, September.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    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:taf:japsta:v:41:y:2014:i:3:p:467-483. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.