IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v132y2014icp94-110.html
   My bibliography  Save this article

Penalized quadratic inference functions for semiparametric varying coefficient partially linear models with longitudinal data

Author

Listed:
  • Tian, Ruiqin
  • Xue, Liugen
  • Liu, Chunling

Abstract

In this paper, we focus on the variable selection for semiparametric varying coefficient partially linear models with longitudinal data. A new variable selection procedure is proposed based on the combination of the basis function approximations and quadratic inference functions. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency and asymptotic normality of the resulting estimators. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedure. We further illustrate the proposed procedure by an application.

Suggested Citation

  • Tian, Ruiqin & Xue, Liugen & Liu, Chunling, 2014. "Penalized quadratic inference functions for semiparametric varying coefficient partially linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 94-110.
    • Handle: RePEc:eee:jmvana:v:132:y:2014:i:c:p:94-110
    DOI: 10.1016/j.jmva.2014.07.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14001729
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.07.015?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. 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. 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.
    4. Xue, Lan & Qu, Annie & Zhou, Jianhui, 2010. "Consistent Model Selection for Marginal Generalized Additive Model for Correlated Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1518-1530.
    5. Yang Bai & Zhongyi Zhu & Wing K. Fung, 2008. "Partial Linear Models for Longitudinal Data Based on Quadratic Inference Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(1), pages 104-118, March.
    6. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    7. 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.
    8. Zhao, Peixin & Xue, Liugen, 2009. "Variable selection for semiparametric varying coefficient partially linear models," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2148-2157, October.
    9. He, Xuming & Fung, Wing K. & Zhu, Zhongyi, 2005. "Robust Estimation in Generalized Partial Linear Models for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1176-1184, December.
    10. Zhang, Wenyang & Lee, Sik-Yum & Song, Xinyuan, 2002. "Local Polynomial Fitting in Semivarying Coefficient Model," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 166-188, July.
    11. 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.
    12. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    13. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
    14. 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.
    15. 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.
    16. Annie Qu & Runze Li, 2006. "Quadratic Inference Functions for Varying-Coefficient Models with Longitudinal Data," Biometrics, The International Biometric Society, vol. 62(2), pages 379-391, June.
    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. Zhongzhe Ouyang & Lu Wang & Alzheimer’s Disease Neuroimaging Initiative, 2024. "Imputation-Based Variable Selection Method for Block-Wise Missing Data When Integrating Multiple Longitudinal Studies," Mathematics, MDPI, vol. 12(7), pages 1-14, March.
    2. Ruiqin Tian & Miaojie Xia & Dengke Xu, 2024. "Profile quasi-maximum likelihood estimation for semiparametric varying-coefficient spatial autoregressive panel models with fixed effects," Statistical Papers, Springer, vol. 65(8), pages 5109-5143, October.
    3. Xin Wang & Xin Zhang, 2024. "Scanner: Simultaneously temporal trend and spatial cluster detection for spatial‐temporal data," Environmetrics, John Wiley & Sons, Ltd., vol. 35(5), August.

    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. 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.
    2. Tang, Yanlin & Wang, Huixia Judy & Zhu, Zhongyi, 2013. "Variable selection in quantile varying coefficient models with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 435-449.
    3. Weihua Zhao & Weiping Zhang & Heng Lian, 2020. "Marginal quantile regression for varying coefficient models with longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 213-234, February.
    4. 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).
    5. Ma, Shujie & Liang, Hua & Tsai, Chih-Ling, 2014. "Partially linear single index models for repeated measurements," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 354-375.
    6. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    7. 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.
    8. Long Feng & Changliang Zou & Zhaojun Wang & Xianwu Wei & Bin Chen, 2015. "Robust spline-based variable selection in varying coefficient model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 85-118, January.
    9. Peixin Zhao & Liugen Xue, 2011. "Variable selection for varying coefficient models with measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 231-245, September.
    10. Zhao, Weihua & Zhang, Riquan & Liu, Jicai & Hu, Hongchang, 2015. "Robust adaptive estimation for semivarying coefficient models," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 132-141.
    11. Sanying Feng & Liugen Xue, 2013. "Variable selection for partially varying coefficient single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2637-2652, December.
    12. Weihua Zhao & Riquan Zhang & Jicai Liu & Yazhao Lv, 2014. "Robust and efficient variable selection for semiparametric partially linear varying coefficient model based on modal regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 165-191, February.
    13. Rui Li & Chenlei Leng & Jinhong You, 2017. "A Semiparametric Regression Model for Longitudinal Data with Non-stationary Errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 932-950, December.
    14. Tian, Ruiqin & Xue, Liugen & Xu, Dengke, 2016. "Automatic variable selection for varying coefficient models with longitudinal data," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 84-90.
    15. Jun Jin & Tiefeng Ma & Jiajia Dai & Shuangzhe Liu, 2021. "Penalized weighted composite quantile regression for partially linear varying coefficient models with missing covariates," Computational Statistics, Springer, vol. 36(1), pages 541-575, March.
    16. Cai, Zongwu & Juhl, Ted & Yang, Bingduo, 2015. "Functional index coefficient models with variable selection," Journal of Econometrics, Elsevier, vol. 189(2), pages 272-284.
    17. 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.
    18. Joseph G. Ibrahim & Hongtu Zhu & Ramon I. Garcia & Ruixin Guo, 2011. "Fixed and Random Effects Selection in Mixed Effects Models," Biometrics, The International Biometric Society, vol. 67(2), pages 495-503, June.
    19. Jingyuan Liu & Runze Li & Rongling Wu, 2014. "Feature Selection for Varying Coefficient Models With Ultrahigh-Dimensional Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 266-274, March.
    20. 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.

    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:132:y:2014:i:c:p:94-110. 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.