IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v94y2007i4p921-937.html
   My bibliography  Save this article

Empirical Likelihood Semiparametric Regression Analysis for Longitudinal Data

Author

Listed:
  • Liugen Xue
  • Lixing Zhu

Abstract

A semiparametric regression model for longitudinal data is considered. The empirical likelihood method is used to estimate the regression coefficients and the baseline function, and to construct confidence regions and intervals. It is proved that the maximum empirical likelihood estimator of the regression coefficients achieves asymptotic efficiency and the estimator of the baseline function attains asymptotic normality when a bias correction is made. Two calibrated empirical likelihood approaches to inference for the baseline function are developed. We propose a groupwise empirical likelihood procedure to handle the inter-series dependence for the longitudinal semiparametric regression model, and employ bias correction to construct the empirical likelihood ratio functions for the parameters of interest. This leads us to prove a nonparametric version of Wilks' theorem. Compared with methods based on normal approximations, the empirical likelihood does not require consistent estimators for the asymptotic variance and bias. A simulation compares the empirical likelihood and normal-based methods in terms of coverage accuracies and average areas/lengths of confidence regions/intervals. Copyright 2007, Oxford University Press.

Suggested Citation

  • Liugen Xue & Lixing Zhu, 2007. "Empirical Likelihood Semiparametric Regression Analysis for Longitudinal Data," Biometrika, Biometrika Trust, vol. 94(4), pages 921-937.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:4:p:921-937
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asm066
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

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

    Citations

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


    Cited by:

    1. Francesco Bravo, 2014. "Varying coefficients partially linear models with randomly censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 383-412, April.
    2. Qian, Lianfen & Wang, Suojin, 2017. "Subject-wise empirical likelihood inference in partial linear models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 77-87.
    3. Peixin Zhao & Xinrong Tang, 2016. "Imputation based statistical inference for partially linear quantile regression models with missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 991-1009, November.
    4. Peixin Zhao & Liugen Xue, 2009. "Empirical likelihood inferences for semiparametric varying-coefficient partially linear errors-in-variables models with longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(7), pages 907-923.
    5. Shuanghua Luo & Yuxin Yan & Cheng-yi Zhang, 2024. "Two-Stage Estimation of Partially Linear Varying Coefficient Quantile Regression Model with Missing Data," Mathematics, MDPI, vol. 12(4), pages 1-15, February.
    6. 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.
    7. Li, Daoji & Pan, Jianxin, 2013. "Empirical likelihood for generalized linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 63-73.
    8. Qin, Guoyou & Bai, Yang & Zhu, Zhongyi, 2012. "Robust empirical likelihood inference for generalized partial linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 32-44.
    9. 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.
    10. 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.
    11. Lai, Peng & Li, Gaorong & Lian, Heng, 2013. "Quadratic inference functions for partially linear single-index models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 115-127.
    12. 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.
    13. Peixin Zhao & Xiaoshuang Zhou, 2018. "Robust empirical likelihood for partially linear models via weighted composite quantile regression," Computational Statistics, Springer, vol. 33(2), pages 659-674, June.
    14. Kangning Wang & Mengjie Hao & Xiaofei Sun, 2021. "Robust and efficient estimating equations for longitudinal data partial linear models and its applications," Statistical Papers, Springer, vol. 62(5), pages 2147-2168, October.
    15. Bindele, Huybrechts F. & Abebe, Ash, 2015. "Semi-parametric rank regression with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 117-132.
    16. Xue, Liugen, 2009. "Empirical likelihood for linear models with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1353-1366, August.
    17. Qin, Guoyou & Bai, Yang & Zhu, Zhongyi, 2009. "Robust empirical likelihood inference for longitudinal data," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2101-2108, October.
    18. Yang, Hu & Li, Tingting, 2010. "Empirical likelihood for semiparametric varying coefficient partially linear models with longitudinal data," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 111-121, January.
    19. 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.
    20. He, Bang-Qiang & Hong, Xing-Jian & Fan, Guo-Liang, 2017. "Block empirical likelihood for partially linear panel data models with fixed effects," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 128-138.
    21. Xiaoshuang Zhou & Peixin Zhao & Yujie Gai, 2022. "Imputation-based empirical likelihood inferences for partially nonlinear quantile regression models with missing responses," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 705-722, December.
    22. 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.
    23. Hengzhen Huang & Guangni Mo & Haiou Li & Hong-Bin Fang, 2022. "Representation Theorem and Functional CLT for RKHS-Based Function-on-Function Regressions," Mathematics, MDPI, vol. 10(14), pages 1-23, July.
    24. 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.
    25. Zhao, Peixin & Xue, Liugen, 2010. "Variable selection for semiparametric varying coefficient partially linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1872-1883, September.

    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:oup:biomet:v:94:y:2007:i:4:p:921-937. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.