IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v66y2014i5p931-960.html
   My bibliography  Save this article

On estimation and inference in a partially linear hazard model with varying coefficients

Author

Listed:
  • Yunbei Ma
  • Alan Wan
  • Xuerong Chen
  • Yong Zhou

Abstract

We study estimation and inference in a marginal proportional hazards model that can handle (1) linear effects, (2) non-linear effects and (3) interactions between covariates. The model under consideration is an amalgamation of three existing marginal proportional hazards models studied in the literature. Developing an estimation and inference procedure with desirable properties for the amalgamated model is rather challenging due to the co-existence of all three effects listed above. Much of the existing literature has avoided the problem by considering narrow versions of the model. The object of this paper is to show that an estimation and inference procedure that accommodates all three effects is within reach. We present a profile partial-likelihood approach for estimating the unknowns in the amalgamated model with the resultant estimators of the unknown parameters being root- $$n$$ n consistent and the estimated functions achieving optimal convergence rates. Asymptotic normality is also established for the estimators. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Yunbei Ma & Alan Wan & Xuerong Chen & Yong Zhou, 2014. "On estimation and inference in a partially linear hazard model with varying coefficients," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 931-960, October.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:5:p:931-960
    DOI: 10.1007/s10463-013-0430-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-013-0430-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-013-0430-0?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. Jianwen Cai & Jianqing Fan & Jiancheng Jiang & Haibo Zhou, 2008. "Partially linear hazard regression with varying coefficients for multivariate survival data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 141-158, February.
    2. Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-548, May.
    3. 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.
    4. Lu Tian & David Zucker & L.J. Wei, 2005. "On the Cox Model With Time-Varying Regression Coefficients," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 172-183, March.
    5. Cai, Jianwen & Fan, Jianqing & Jiang, Jiancheng & Zhou, Haibo, 2007. "Partially Linear Hazard Regression for Multivariate Survival Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 538-551, 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. 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.
    2. Qiu, Zhiping & Zhou, Yong, 2015. "Partially linear transformation models with varying coefficients for multivariate failure time data," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 144-166.
    3. Liu, Jicai & Zhang, Riquan & Zhao, Weihua & Lv, Yazhao, 2015. "Variable selection in semiparametric hazard regression for multivariate survival data," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 26-40.
    4. repec:hum:wpaper:sfb649dp2012-061 is not listed on IDEAS
    5. Honda, Toshio & Härdle, Wolfgang Karl, 2012. "Variable selection in Cox regression models with varying coefficients," SFB 649 Discussion Papers 2012-061, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Jun Yan & Jian Huang, 2012. "Model Selection for Cox Models with Time-Varying Coefficients," Biometrics, The International Biometric Society, vol. 68(2), pages 419-428, June.
    7. Lian, Heng & Li, Jianbo & Hu, Yuao, 2013. "Shrinkage variable selection and estimation in proportional hazards models with additive structure and high dimensionality," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 99-112.
    8. De Luca, Giuseppe & Magnus, Jan R. & Peracchi, Franco, 2018. "Weighted-average least squares estimation of generalized linear models," Journal of Econometrics, Elsevier, vol. 204(1), pages 1-17.
    9. Yongxiu Cao & Jian Huang & Yanyan Liu & Xingqiu Zhao, 2016. "Sieve estimation of Cox models with latent structures," Biometrics, The International Biometric Society, vol. 72(4), pages 1086-1097, December.
    10. Jun Jin & Tiefeng Ma & Jiajia Dai, 2021. "New efficient spline estimation for varying-coefficient models with two-step knot number selection," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 693-712, July.
    11. Jianwen Cai & Jianqing Fan & Jiancheng Jiang & Haibo Zhou, 2008. "Partially linear hazard regression with varying coefficients for multivariate survival data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 141-158, February.
    12. Xiaomeng Qi & Zhangsheng Yu, 2023. "Kernel regression for cause-specific hazard models with time-dependent coefficients," Computational Statistics, Springer, vol. 38(1), pages 263-283, March.
    13. 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.
    14. Huazhen Lin & Hyokyoung G. Hong & Baoying Yang & Wei Liu & Yong Zhang & Gang-Zhi Fan & Yi Li, 2019. "Nonparametric Time-Varying Coefficient Models for Panel Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(3), pages 548-566, December.
    15. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    16. Guan, Wei & Gray, Alexander, 2013. "Sparse high-dimensional fractional-norm support vector machine via DC programming," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 136-148.
    17. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    18. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
    19. Xu, Yang & Zhao, Shishun & Hu, Tao & Sun, Jianguo, 2021. "Variable selection for generalized odds rate mixture cure models with interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    20. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    21. Hongyuan Cao & Mathew M. Churpek & Donglin Zeng & Jason P. Fine, 2015. "Analysis of the Proportional Hazards Model With Sparse Longitudinal Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1187-1196, September.

    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:spr:aistmt:v:66:y:2014:i:5:p:931-960. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.