IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v178y2023ics016794732200189x.html
   My bibliography  Save this article

Smoothed tensor quantile regression estimation for longitudinal data

Author

Listed:
  • Ke, Baofang
  • Zhao, Weihua
  • Wang, Lei

Abstract

As extensions of vector and matrix data with ultrahigh dimensionality and complex structures, tensor data are fast emerging in a large variety of scientific applications. In this paper, a two-stage estimation procedure for linear tensor quantile regression (QR) with longitudinal data is proposed. In the first stage, we account for within-subject correlations by using the generalized estimating equations and then impose a low-rank assumption on tensor coefficients to reduce the number of parameters by a canonical polyadic decomposition. To avoid the asymptotic analysis and computation problems caused by the non-smooth QR score function, kernel smoothing method is applied in the second stage to construct the smoothed tensor QR estimator. When the number of rank is given, a block-relaxation algorithm is proposed to estimate the regression coefficients. A modified BIC is applied to estimate the number of rank in practice and show the rank selection consistency. Further, a regularized estimator and its algorithm are investigated for better interpretation and efficiency. The asymptotic properties of the proposed estimators are established. Simulation studies and a real example on Beijing Air Quality data set are provided to show the performance of the proposed estimators.

Suggested Citation

  • Ke, Baofang & Zhao, Weihua & Wang, Lei, 2023. "Smoothed tensor quantile regression estimation for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:csdana:v:178:y:2023:i:c:s016794732200189x
    DOI: 10.1016/j.csda.2022.107609
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016794732200189X
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2022.107609?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. Whang, Yoon-Jae, 2006. "Smoothed Empirical Likelihood Methods For Quantile Regression Models," Econometric Theory, Cambridge University Press, vol. 22(2), pages 173-205, April.
    2. Xiaoshan Li & Da Xu & Hua Zhou & Lexin Li, 2018. "Tucker Tensor Regression and Neuroimaging Analysis," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 520-545, December.
    3. Lan Wang & Jianhui Zhou & Annie Qu, 2012. "Penalized Generalized Estimating Equations for High-Dimensional Longitudinal Data Analysis," Biometrics, The International Biometric Society, vol. 68(2), pages 353-360, June.
    4. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    5. Otsu, Taisuke, 2008. "Conditional empirical likelihood estimation and inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 142(1), pages 508-538, January.
    6. 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.
    7. Li, Jianbo & Lian, Heng & Jiang, Xuejun & Song, Xinyuan, 2018. "Estimation and testing for time-varying quantile single-index models with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 118(C), pages 66-83.
    8. Zhang, Ting & Wang, Lei, 2020. "Smoothed empirical likelihood inference and variable selection for quantile regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    10. 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.
    11. Hua Zhou & Lexin Li & Hongtu Zhu, 2013. "Tensor Regression with Applications in Neuroimaging Data Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 540-552, June.
    12. Jianhui Zhou & Annie Qu, 2012. "Informative Estimation and Selection of Correlation Structure for Longitudinal Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 701-710, June.
    13. Will Wei Sun & Junwei Lu & Han Liu & Guang Cheng, 2017. "Provable sparse tensor decomposition," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 899-916, 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. Hou, Zhaohan & Wang, Lei, 2024. "Heterogeneous quantile regression for longitudinal data with subgroup structures," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    2. Zhang, Ting & Wang, Lei, 2020. "Smoothed empirical likelihood inference and variable selection for quantile regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    3. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    4. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(1), pages 74-113, February.
    5. Tang, Cheng Yong & Leng, Chenlei, 2012. "An empirical likelihood approach to quantile regression with auxiliary information," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 29-36.
    6. Marcelo Fernandes & Emmanuel Guerre & Eduardo Horta, 2021. "Smoothing Quantile Regressions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 338-357, January.
    7. Conde-Amboage, Mercedes & Sánchez-Sellero, César & González-Manteiga, Wenceslao, 2015. "A lack-of-fit test for quantile regression models with high-dimensional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 128-138.
    8. Philip Kostov, 2013. "Empirical likelihood estimation of the spatial quantile regression," Journal of Geographical Systems, Springer, vol. 15(1), pages 51-69, January.
    9. Shuanghua Luo & Changlin Mei & Cheng-yi Zhang, 2017. "Smoothed empirical likelihood for quantile regression models with response data missing at random," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(1), pages 95-116, January.
    10. Kangning Wang & Lu Lin, 2017. "Robust and efficient direction identification for groupwise additive multiple-index models and its applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 22-45, March.
    11. Kaplan, David M. & Sun, Yixiao, 2017. "Smoothed Estimating Equations For Instrumental Variables Quantile Regression," Econometric Theory, Cambridge University Press, vol. 33(1), pages 105-157, February.
    12. Jiang, Rong & Qian, Weimin & Zhou, Zhangong, 2012. "Variable selection and coefficient estimation via composite quantile regression with randomly censored data," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 308-317.
    13. Escanciano, J.C. & Goh, S.C., 2014. "Specification analysis of linear quantile models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 495-507.
    14. 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.
    15. Bang, Sungwan & Jhun, Myoungshic, 2012. "Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 813-826.
    16. Yao, Fang & Sue-Chee, Shivon & Wang, Fan, 2017. "Regularized partially functional quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 39-56.
    17. Zou, Hui & Yuan, Ming, 2008. "Regularized simultaneous model selection in multiple quantiles regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5296-5304, August.
    18. Kean Ming Tan & Lan Wang & Wen‐Xin Zhou, 2022. "High‐dimensional quantile regression: Convolution smoothing and concave regularization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(1), pages 205-233, February.
    19. Alexander Aue & Rex C. Y. Cheung & Thomas C. M. Lee & Ming Zhong, 2014. "Segmented Model Selection in Quantile Regression Using the Minimum Description Length Principle," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1241-1256, September.
    20. Jiang, Rong & Qian, Wei-Min, 2016. "Quantile regression for single-index-coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 305-317.

    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:csdana:v:178:y:2023:i:c:s016794732200189x. 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/locate/csda .

    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.