IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v82y2019i6d10.1007_s00184-018-0699-3.html
   My bibliography  Save this article

Composite quantile estimation in partial functional linear regression model with dependent errors

Author

Listed:
  • Ping Yu

    (Fudan University
    Shanxi Normal University)

  • Ting Li

    (Fudan University)

  • Zhongyi Zhu

    (Fudan University)

  • Zhongzhan Zhang

    (Beijing University of Technology)

Abstract

In this paper, we consider composite quantile estimation for the partial functional linear regression model with errors from a short-range dependent and strictly stationary linear processes. The functional principal component analysis method is employed to estimate the slope function and the functional predictive variable, respectively. Under some regularity conditions, we obtain the optimal convergence rate of the slope function, and the asymptotic normality of the parameter vector. Simulation studies demonstrate that the proposed new estimation method is robust and works much better than the least squares based method when there are outliers in the dataset or the autoregressive error distribution follows a heavy-tailed distribution. Finally, we apply the proposed methodology to electricity consumption data.

Suggested Citation

  • Ping Yu & Ting Li & Zhongyi Zhu & Zhongzhan Zhang, 2019. "Composite quantile estimation in partial functional linear regression model with dependent errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 633-656, August.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:6:d:10.1007_s00184-018-0699-3
    DOI: 10.1007/s00184-018-0699-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-018-0699-3
    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/s00184-018-0699-3?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. Liwen Zhang & Huixia Judy Wang & Zhongyi Zhu, 2017. "Composite change point estimation for bent line quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 145-168, February.
    2. Ping Yu & Zhongzhan Zhang & Jiang Du, 2016. "A test of linearity in partial functional linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 953-969, November.
    3. Ying Lu & Jiang Du & Zhimeng Sun, 2014. "Functional partially linear quantile regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 317-332, February.
    4. Yanlin Tang & Xinyuan Song & Zhongyi Zhu, 2015. "Variable selection via composite quantile regression with dependent errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 1-20, February.
    5. Kehui Chen & Hans‐Georg Müller, 2012. "Conditional quantile analysis when covariates are functions, with application to growth data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 67-89, January.
    6. Beran, Jan & Liu, Haiyan, 2016. "Estimation of eigenvalues, eigenvectors and scores in FDA models with dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 218-233.
    7. Imaizumi, Masaaki & Kato, Kengo, 2018. "PCA-based estimation for functional linear regression with functional responses," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 15-36.
    8. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
    9. Dehan Kong & Kaijie Xue & Fang Yao & Hao H. Zhang, 2016. "Partially functional linear regression in high dimensions," Biometrika, Biometrika Trust, vol. 103(1), pages 147-159.
    10. Germán Aneiros & Paula Raña & Philippe Vieu & Juan Vilar, 2018. "Bootstrap in semi-functional partial linear regression under dependence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 659-679, September.
    11. Jianjun Zhou & Zhao Chen & Qingyan Peng, 2016. "Polynomial spline estimation for partial functional linear regression models," Computational Statistics, Springer, vol. 31(3), pages 1107-1129, September.
    12. Peter Hall & Giles Hooker, 2016. "Truncated linear models for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 637-653, 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. Bin Yang & Min Chen & Tong Su & Jianjun Zhou, 2023. "Robust Estimation for Semi-Functional Linear Model with Autoregressive Errors," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    2. Hao Cheng, 2023. "Composite quantile estimation in PLS-SEM for environment sustainable development evaluation," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 25(7), pages 6249-6268, July.

    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. Ping Yu & Zhongyi Zhu & Zhongzhan Zhang, 2019. "Robust exponential squared loss-based estimation in semi-functional linear regression models," Computational Statistics, Springer, vol. 34(2), pages 503-525, June.
    2. Guodong Shan & Yiheng Hou & Baisen Liu, 2020. "Bayesian robust estimation of partially functional linear regression models using heavy-tailed distributions," Computational Statistics, Springer, vol. 35(4), pages 2077-2092, December.
    3. Tang, Qingguo & Tu, Wei & Kong, Linglong, 2023. "Estimation for partial functional partially linear additive model," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    4. Liebl, Dominik & Walders, Fabian, 2019. "Parameter regimes in partial functional panel regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 105-115.
    5. Zhu, Hanbing & Zhang, Riquan & Yu, Zhou & Lian, Heng & Liu, Yanghui, 2019. "Estimation and testing for partially functional linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 296-314.
    6. Yuping Hu & Siyu Wu & Sanying Feng & Junliang Jin, 2020. "Estimation in Partial Functional Linear Spatial Autoregressive Model," Mathematics, MDPI, vol. 8(10), pages 1-12, October.
    7. Yu, Dengdeng & Zhang, Li & Mizera, Ivan & Jiang, Bei & Kong, Linglong, 2019. "Sparse wavelet estimation in quantile regression with multiple functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 12-29.
    8. Rongjie Jiang & Liming Wang & Yang Bai, 2021. "Optimal model averaging estimator for semi-functional partially linear models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(2), pages 167-194, February.
    9. Ma, Haiqiang & Li, Ting & Zhu, Hongtu & Zhu, Zhongyi, 2019. "Quantile regression for functional partially linear model in ultra-high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 135-147.
    10. Sang, Peijun & Lockhart, Richard A. & Cao, Jiguo, 2018. "Sparse estimation for functional semiparametric additive models," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 105-118.
    11. Sanying Feng & Menghan Zhang & Tiejun Tong, 2022. "Variable selection for functional linear models with strong heredity constraint," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 321-339, April.
    12. Yang, Seong J. & Shin, Hyejin & Lee, Sang Han & Lee, Seokho, 2020. "Functional linear regression model with randomly censored data: Predicting conversion time to Alzheimer ’s disease," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    13. Xiongtao Dai & Zhenhua Lin & Hans‐Georg Müller, 2021. "Modeling sparse longitudinal data on Riemannian manifolds," Biometrics, The International Biometric Society, vol. 77(4), pages 1328-1341, December.
    14. Zhang, Xiaochen & Zhang, Qingzhao & Ma, Shuangge & Fang, Kuangnan, 2022. "Subgroup analysis for high-dimensional functional regression," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    15. Liang, Weijuan & Zhang, Qingzhao & Ma, Shuangge, 2023. "Locally sparse quantile estimation for a partially functional interaction model," Computational Statistics & Data Analysis, Elsevier, vol. 186(C).
    16. Fanrong Zhao & Baoxue Zhang, 2024. "A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model," Mathematics, MDPI, vol. 12(16), pages 1-24, August.
    17. Aneiros, Germán & Novo, Silvia & Vieu, Philippe, 2022. "Variable selection in functional regression models: A review," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    18. Yousri Slaoui, 2020. "Recursive nonparametric regression estimation for dependent strong mixing functional data," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 665-697, October.
    19. Chang, Jinyuan & Chen, Cheng & Qiao, Xinghao & Yao, Qiwei, 2023. "An autocovariance-based learning framework for high-dimensional functional time series," LSE Research Online Documents on Economics 117910, London School of Economics and Political Science, LSE Library.
    20. Ding, Hui & Lu, Zhiping & Zhang, Jian & Zhang, Riquan, 2018. "Semi-functional partial linear quantile regression," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 92-101.

    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:metrik:v:82:y:2019:i:6:d:10.1007_s00184-018-0699-3. 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.