IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v62y2021i5d10.1007_s00362-020-01181-5.html
   My bibliography  Save this article

Robust and efficient estimating equations for longitudinal data partial linear models and its applications

Author

Listed:
  • Kangning Wang

    (Shandong Technology and Business University)

  • Mengjie Hao

    (Shandong Technology and Business University)

  • Xiaofei Sun

    (Shandong Technology and Business University)

Abstract

Composite quantile regression (CQR) is a good alternative of the mean regression, because of its robustness and efficiency. In longitudinal data analysis, correlation structure plays an important role in improving efficiency. However, how to specify the correlation matrix in CQR with longitudinal data is challenging. We propose a new approach that uses copula to account for intra-subject dependence, and by using the copula based covariance matrix, robust and efficient CQR estimating equations are constructed for the partial linear models with longitudinal data. As a specific application, a copula based CQR empirical likelihood is proposed. Furthermore, it can also be used to develop a penalized empirical likelihood for variable selection. Our proposed new methods are flexible, and can provide robust and efficient estimation. The properties of the proposed methods are established theoretically, and assessed numerically through simulation studies.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:5:d:10.1007_s00362-020-01181-5
    DOI: 10.1007/s00362-020-01181-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-020-01181-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-020-01181-5?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. Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo, 2010. "On the simplified pair-copula construction -- Simply useful or too simplistic?," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1296-1310, May.
    2. Kangning Wang & Lu Lin, 2019. "Robust and efficient estimator for simultaneous model structure identification and variable selection in generalized partial linear varying coefficient models with longitudinal data," Statistical Papers, Springer, vol. 60(5), pages 1649-1676, October.
    3. Rong Jiang & Wei-Min Qian & Zhan-Gong Zhou, 2016. "Single-index composite quantile regression with heteroscedasticity and general error distributions," Statistical Papers, Springer, vol. 57(1), pages 185-203, March.
    4. Peter Xue‐Kun Song, 2000. "Multivariate Dispersion Models Generated From Gaussian Copula," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 305-320, June.
    5. Bo Kai & Runze Li & Hui Zou, 2010. "Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 49-69, January.
    6. 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.
    7. B. M. Brown & You-Gan Wang, 2005. "Standard errors and covariance matrices for smoothed rank estimators," Biometrika, Biometrika Trust, vol. 92(1), pages 149-158, March.
    8. 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.
    9. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    10. 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.
    11. Smith, Michael & Min, Aleksey & Almeida, Carlos & Czado, Claudia, 2010. "Modeling Longitudinal Data Using a Pair-Copula Decomposition of Serial Dependence," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1467-1479.
    12. Zhang, Jun & Zhou, Yan & Lin, Bingqing & Yu, Yao, 2017. "Estimation and hypothesis test on partial linear models with additive distortion measurement errors," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 114-128.
    13. Fan, Yali & Qin, Guoyou & Zhu, Zhongyi, 2012. "Variable selection in robust regression models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 156-167.
    14. Qin, Guoyou & Zhu, Zhongyi, 2007. "Robust estimation in generalized semiparametric mixed models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1658-1683, September.
    15. Lv, Jing & Yang, Hu & Guo, Chaohui, 2015. "An efficient and robust variable selection method for longitudinal generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 74-88.
    16. Sun, Jiafeng & Frees, Edward W. & Rosenberg, Marjorie A., 2008. "Heavy-tailed longitudinal data modeling using copulas," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 817-830, April.
    17. 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.
    18. Liugen Xue & Lixing Zhu, 2007. "Empirical Likelihood Semiparametric Regression Analysis for Longitudinal Data," Biometrika, Biometrika Trust, vol. 94(4), pages 921-937.
    19. Chen, Kani & Jin, Zhezhen, 2006. "Partial Linear Regression Models for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 195-204, March.
    20. Fu, Liya & Wang, You-Gan, 2016. "Efficient parameter estimation via Gaussian copulas for quantile regression with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 492-502.
    21. Xiaolin Chen & Xiaojing Chen & Yi Liu, 2019. "A note on quantile feature screening via distance correlation," Statistical Papers, Springer, vol. 60(5), pages 1741-1762, October.
    22. Yan Fan & Wolfgang Karl Härdle & Weining Wang & Lixing Zhu, 2018. "Single-Index-Based CoVaR With Very High-Dimensional Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 212-226, April.
    23. Yun Bai & Jian Kang & Peter X.-K. Song, 2014. "Efficient pairwise composite likelihood estimation for spatial-clustered data," Biometrics, The International Biometric Society, vol. 70(3), pages 661-670, September.
    24. Li, Gaorong & Lian, Heng & Feng, Sanying & Zhu, Lixing, 2013. "Automatic variable selection for longitudinal generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 174-186.
    25. Zhao, Weihua & Lian, Heng & Song, Xinyuan, 2017. "Composite quantile regression for correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 15-33.
    26. Lai, Peng & Wang, Qihua & Lian, Heng, 2012. "Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 422-432.
    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. Kangning Wang & Wen Shan, 2021. "Copula and composite quantile regression-based estimating equations for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 441-455, June.
    2. 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.
    3. Wang, Kangning & Li, Shaomin & Zhang, Benle, 2021. "Robust communication-efficient distributed composite quantile regression and variable selection for massive data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    4. Kangning Wang & Lu Lin, 2019. "Robust and efficient estimator for simultaneous model structure identification and variable selection in generalized partial linear varying coefficient models with longitudinal data," Statistical Papers, Springer, vol. 60(5), pages 1649-1676, October.
    5. 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.
    6. Lv, Jing & Yang, Hu & Guo, Chaohui, 2015. "An efficient and robust variable selection method for longitudinal generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 74-88.
    7. Smith, Michael Stanley, 2015. "Copula modelling of dependence in multivariate time series," International Journal of Forecasting, Elsevier, vol. 31(3), pages 815-833.
    8. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    9. Mozhgan Taavoni & Mohammad Arashi & Samuel Manda, 2023. "Multicollinearity and Linear Predictor Link Function Problems in Regression Modelling of Longitudinal Data," Mathematics, MDPI, vol. 11(3), pages 1-9, January.
    10. Michael Stanley Smith, 2021. "Implicit Copulas: An Overview," Papers 2109.04718, arXiv.org.
    11. Brendan K. Beare & Juwon Seo, 2015. "Vine Copula Specifications for Stationary Multivariate Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 228-246, March.
    12. Nguyen, Hoang & Ausín, M. Concepción & Galeano, Pedro, 2020. "Variational inference for high dimensional structured factor copulas," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    13. Weiping Zhang & MengMeng Zhang & Yu Chen, 2020. "A Copula-Based GLMM Model for Multivariate Longitudinal Data with Mixed-Types of Responses," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 353-379, November.
    14. Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo & Lacal, Virginia, 2016. "Structure learning in Bayesian Networks using regular vines," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 186-208.
    15. Zhao, Weihua & Lian, Heng & Song, Xinyuan, 2017. "Composite quantile regression for correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 15-33.
    16. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    17. Rong Jiang & Mengxian Sun, 2022. "Single-index composite quantile regression for ultra-high-dimensional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 443-460, June.
    18. Kim, Daeyoung & Kim, Jong-Min & Liao, Shu-Min & Jung, Yoon-Sung, 2013. "Mixture of D-vine copulas for modeling dependence," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 1-19.
    19. 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.
    20. 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.

    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:stpapr:v:62:y:2021:i:5:d:10.1007_s00362-020-01181-5. 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.