IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v121y2013icp22-32.html
   My bibliography  Save this article

Empirical likelihood for partially linear proportional hazards models with growing dimensions

Author

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

Abstract

Empirical-likelihood-based inferences for the linear part in a partially linear Cox’s proportional hazards model are investigated. It was shown in some previous studies, for some related but different semiparametric models, that if there is no bias correction, the limit distribution of the empirical likelihood ratio statistic is not a standard chi-square distribution. In some previous studies, the bias correction is achieved by subtracting a conditional expectation of a predictor from itself. In proportional hazards models, the situation is different and it is not clear how to do so. Motivated from the form of the asymptotic variance of the parameters, the bias-corrected empirical likelihood ratio is proposed, with a standard χ2 limit. The demonstrated asymptotics even apply to models with growing dimensions. For computational simplicity, we use polynomial splines to approximate the nonparametric component so that the computations involved are similar to those for the parametric model. Some simulations are carried out to study the performance of bias-corrected empirical likelihood ratio.

Suggested Citation

  • Tang, Xingyu & Li, Jianbo & Lian, Heng, 2013. "Empirical likelihood for partially linear proportional hazards models with growing dimensions," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 22-32.
    • Handle: RePEc:eee:jmvana:v:121:y:2013:i:c:p:22-32
    DOI: 10.1016/j.jmva.2013.06.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13001140
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.06.002?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. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
    2. Xue, Liugen & Zhu, Lixing, 2007. "Empirical Likelihood for a Varying Coefficient Model With Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 642-654, June.
    3. Nielsen, Jens P. & Linton, Oliver & Bickel, Peter J., 1998. "On a semiparametric survival model with flexible covariate effect," LSE Research Online Documents on Economics 301, London School of Economics and Political Science, LSE Library.
    4. Xue, Liu-Gen & Zhu, Lixing, 2006. "Empirical likelihood for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1295-1312, July.
    5. Li, Gaorong & Lin, Lu & Zhu, Lixing, 2012. "Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 85-111.
    6. Chenlei Leng & Cheng Yong Tang, 2012. "Penalized empirical likelihood and growing dimensional general estimating equations," Biometrika, Biometrika Trust, vol. 99(3), pages 703-716.
    7. Li, Gaorong & Zhu, Lixing & Xue, Liugen & Feng, Sanying, 2010. "Empirical likelihood inference in partially linear single-index models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 718-732, March.
    8. Zhu, Lixing & Lin, Lu & Cui, Xia & Li, Gaorong, 2010. "Bias-corrected empirical likelihood in a multi-link semiparametric model," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 850-868, April.
    9. Huang, Zhensheng & Pang, Zhen & Zhang, Riquan, 2013. "Adaptive profile-empirical-likelihood inferences for generalized single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 70-82.
    10. Liugen Xue & Lixing Zhu, 2007. "Empirical Likelihood Semiparametric Regression Analysis for Longitudinal Data," Biometrika, Biometrika Trust, vol. 94(4), pages 921-937.
    11. Song Xi Chen & Liang Peng & Ying-Li Qin, 2009. "Effects of data dimension on empirical likelihood," Biometrika, Biometrika Trust, vol. 96(3), pages 711-722.
    12. Huang, Zhensheng & Zhang, Riquan, 2011. "Efficient empirical-likelihood-based inferences for the single-index model," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 937-947, May.
    13. Yanqing Sun & Rajeshwari Sundaram & Yichuan Zhao, 2009. "Empirical Likelihood Inference for the Cox Model with Time‐dependent Coefficients via Local Partial Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 444-462, September.
    14. Cheng Yong Tang & Chenlei Leng, 2010. "Penalized high-dimensional empirical likelihood," Biometrika, Biometrika Trust, vol. 97(4), pages 905-920.
    15. You, Jinhong & Zhou, Yong, 2006. "Empirical likelihood for semiparametric varying-coefficient partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 412-422, February.
    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. Lei Wang & Wei Ma, 2021. "Improved empirical likelihood inference and variable selection for generalized linear models with longitudinal nonignorable dropouts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 623-647, June.
    2. Ming-Yueh Huang & Kwun Chuen Gary Chan, 2022. "Model selection among Dimension-Reduced generalized Cox models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(3), pages 492-511, July.
    3. Yujing Shao & Lei Wang, 2022. "Generalized partial linear models with nonignorable dropouts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 223-252, February.

    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. Yang, Yiping & Li, Gaorong & Peng, Heng, 2014. "Empirical likelihood of varying coefficient errors-in-variables models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 1-18.
    2. Li, Gaorong & Lin, Lu & Zhu, Lixing, 2012. "Empirical likelihood for a varying coefficient partially linear model with diverging number of parameters," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 85-111.
    3. Li, Gao-Rong & Zhu, Li-Ping & Zhu, Li-Xing, 2010. "Adaptive confidence region for the direction in semiparametric regressions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1364-1377, July.
    4. Fan, Guo-Liang & Liang, Han-Ying & Shen, Yu, 2016. "Penalized empirical likelihood for high-dimensional partially linear varying coefficient model with measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 183-201.
    5. Feng, Sanying & Lian, Heng & Zhu, Fukang, 2016. "Reduced rank regression with possibly non-smooth criterion functions: An empirical likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 139-150.
    6. Wang, Kangning & Li, Shaomin & Sun, Xiaofei & Lin, Lu, 2019. "Modal regression statistical inference for longitudinal data semivarying coefficient models: Generalized estimating equations, empirical likelihood and variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 257-276.
    7. Li, Gaorong & Zhu, Lixing & Xue, Liugen & Feng, Sanying, 2010. "Empirical likelihood inference in partially linear single-index models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 718-732, March.
    8. Hong Guo & Changliang Zou & Zhaojun Wang & Bin Chen, 2014. "Empirical likelihood for high-dimensional linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(7), pages 921-945, October.
    9. Xue, Liugen, 2009. "Empirical likelihood for linear models with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1353-1366, August.
    10. 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.
    11. Liugen Xue, 2010. "Empirical Likelihood Local Polynomial Regression Analysis of Clustered Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 644-663, December.
    12. Zhang, Jia & Shi, Haoming & Tian, Lemeng & Xiao, Fengjun, 2019. "Penalized generalized empirical likelihood in high-dimensional weakly dependent data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 270-283.
    13. Li, Yujie & Li, Gaorong & Lian, Heng & Tong, Tiejun, 2017. "Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 133-150.
    14. Liugen Xue, 2009. "Empirical Likelihood Confidence Intervals for Response Mean with Data Missing at Random," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 671-685, December.
    15. Xue, Liugen & Xue, Dong, 2011. "Empirical likelihood for semiparametric regression model with missing response data," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 723-740, April.
    16. Tong Tong Wu & Gang Li & Chengyong Tang, 2015. "Empirical Likelihood for Censored Linear Regression and Variable Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 798-812, September.
    17. Peixin Zhao & Liugen Xue, 2012. "Variable selection in semiparametric regression analysis for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 213-231, February.
    18. Zhensheng Huang & Xing Sun & Riquan Zhang, 2022. "Estimation for partially varying-coefficient single-index models with distorted measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 175-201, February.
    19. Qinqin Hu & Lu Lin, 2017. "Conditional sure independence screening by conditional marginal empirical likelihood," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 63-96, February.
    20. Li, Gaorong & Feng, Sanying & Peng, Heng, 2011. "A profile-type smoothed score function for a varying coefficient partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 372-385, February.

    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:121:y:2013:i:c:p:22-32. 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.