IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v190y2022ics0047259x22000264.html
   My bibliography  Save this article

Inference in functional linear quantile regression

Author

Listed:
  • Li, Meng
  • Wang, Kehui
  • Maity, Arnab
  • Staicu, Ana-Maria

Abstract

In this paper, we study statistical inference in functional quantile regression for scalar response and a functional covariate. Specifically, we consider a functional linear quantile regression model where the effect of the covariate on the quantile of the response is modeled through the inner product between the functional covariate and an unknown smooth regression parameter function that varies with the level of quantile. The objective is to test that the regression parameter is constant across several quantile levels of interest. The parameter function is estimated by combining ideas from functional principal component analysis and quantile regression. An adjusted Wald testing procedure is proposed for this hypothesis of interest, and its chi-square asymptotic null distribution is derived. The testing procedure is investigated numerically in simulations involving sparse and noisy functional covariates and in a capital bike share data application. The proposed approach is easy to implement and the R code is published online at https://github.com/xylimeng/fQR-testing.

Suggested Citation

  • Li, Meng & Wang, Kehui & Maity, Arnab & Staicu, Ana-Maria, 2022. "Inference in functional linear quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:jmvana:v:190:y:2022:i:c:s0047259x22000264
    DOI: 10.1016/j.jmva.2022.104985
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X22000264
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2022.104985?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. Ana-Maria Staicu & Ciprian M. Crainiceanu & Daniel S. Reich & David Ruppert, 2012. "Modeling Functional Data with Spatially Heterogeneous Shape Characteristics," Biometrics, The International Biometric Society, vol. 68(2), pages 331-343, June.
    2. Yao, Fang & Sue-Chee, Shivon & Wang, Fan, 2017. "Regularized partially functional quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 39-56.
    3. 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.
    4. Crambes, Christophe & Gannoun, Ali & Henchiri, Yousri, 2013. "Support vector machine quantile regression approach for functional data: Simulation and application studies," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 50-68.
    5. Zhao, Zhibiao & Xiao, Zhijie, 2014. "Efficient Regressions Via Optimally Combining Quantile Information," Econometric Theory, Cambridge University Press, vol. 30(6), pages 1272-1314, December.
    6. Wei, Ying & Carroll, Raymond J., 2009. "Quantile Regression With Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1129-1143.
    7. Dehan Kong & Ana-Maria Staicu & Arnab Maity, 2016. "Classical testing in functional linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 813-838, October.
    8. Yehua Li & Naisyin Wang & Raymond J. Carroll, 2013. "Selecting the Number of Principal Components in Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1284-1294, December.
    9. Usset, Joseph & Staicu, Ana-Maria & Maity, Arnab, 2016. "Interaction models for functional regression," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 317-329.
    10. Yu-Ru Su & Chong-Zhi Di & Li Hsu, 2017. "Hypothesis testing in functional linear models," Biometrics, The International Biometric Society, vol. 73(2), pages 551-561, June.
    11. Jiang, Liewen & Bondell, Howard D. & Wang, Huixia Judy, 2014. "Interquantile shrinkage and variable selection in quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 208-219.
    12. Yuanshan Wu & Yanyuan Ma & Guosheng Yin, 2015. "Smoothed and Corrected Score Approach to Censored Quantile Regression With Measurement Errors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1670-1683, December.
    13. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    14. Li, Yehua & Wang, Naisyin & Carroll, Raymond J., 2010. "Generalized Functional Linear Models With Semiparametric Single-Index Interactions," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 621-633.
    15. Li, Youjuan & Liu, Yufeng & Zhu, Ji, 2007. "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 255-268, March.
    16. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    17. Huixia Judy Wang & Leonard A. Stefanski & Zhongyi Zhu, 2012. "Corrected-loss estimation for quantile regression with covariate measurement errors," Biometrika, Biometrika Trust, vol. 99(2), pages 405-421.
    18. Jeffrey S. Morris & Raymond J. Carroll, 2006. "Wavelet‐based functional mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 179-199, April.
    19. Hongxiao Zhu & Fang Yao & Hao Helen Zhang, 2014. "Structured functional additive regression in reproducing kernel Hilbert spaces," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 581-603, June.
    20. Andrada Ivanescu & Ana-Maria Staicu & Fabian Scheipl & Sonja Greven, 2015. "Penalized function-on-function regression," Computational Statistics, Springer, vol. 30(2), pages 539-568, June.
    21. Koenker, Roger, 1984. "A note on L-estimates for linear models," Statistics & Probability Letters, Elsevier, vol. 2(6), pages 323-325, December.
    22. Eun Ryung Lee & Hohsuk Noh & Byeong U. Park, 2014. "Model Selection via Bayesian Information Criterion for Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 216-229, March.
    23. Lan Zhou & Jianhua Z. Huang & Raymond J. Carroll, 2008. "Joint modelling of paired sparse functional data using principal components," Biometrika, Biometrika Trust, vol. 95(3), pages 601-619.
    24. Peter Hall & Mohammad Hosseini‐Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126, February.
    25. Crambes, Christophe & Gannoun, Ali & Henchiri, Yousri, 2011. "Weak consistency of the Support Vector Machine Quantile Regression approach when covariates are functions," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1847-1858.
    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. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Ufuk Beyaztas & Han Lin Shang & Aylin Alin, 2022. "Function-on-Function Partial Quantile Regression," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(1), pages 149-174, March.
    3. Xu, Jianjun & Cui, Wenquan, 2022. "A new RKHS-based global testing for functional linear model," Statistics & Probability Letters, Elsevier, vol. 182(C).
    4. Yao, Fang & Sue-Chee, Shivon & Wang, Fan, 2017. "Regularized partially functional quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 39-56.
    5. Jadhav, Sneha & Ma, Shuangge, 2021. "An association test for functional data based on Kendall’s Tau," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    6. Dehan Kong & Joseph G. Ibrahim & Eunjee Lee & Hongtu Zhu, 2018. "FLCRM: Functional linear cox regression model," Biometrics, The International Biometric Society, vol. 74(1), pages 109-117, March.
    7. Kyunghee Han & Pantelis Z Hadjipantelis & Jane-Ling Wang & Michael S Kramer & Seungmi Yang & Richard M Martin & Hans-Georg Müller, 2018. "Functional principal component analysis for identifying multivariate patterns and archetypes of growth, and their association with long-term cognitive development," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-18, November.
    8. Kehui Chen & Xiaoke Zhang & Alexander Petersen & Hans-Georg Müller, 2017. "Quantifying Infinite-Dimensional Data: Functional Data Analysis in Action," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 582-604, December.
    9. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.
    10. Liu, Yanghui & Li, Yehua & Carroll, Raymond J. & Wang, Naisyin, 2022. "Predictive functional linear models with diverging number of semiparametric single-index interactions," Journal of Econometrics, Elsevier, vol. 230(2), pages 221-239.
    11. 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.
    12. Chenlin Zhang & Huazhen Lin & Li Liu & Jin Liu & Yi Li, 2023. "Functional data analysis with covariate‐dependent mean and covariance structures," Biometrics, The International Biometric Society, vol. 79(3), pages 2232-2245, September.
    13. 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.
    14. Saart, Patrick W. & Xia, Yingcun, 2022. "Functional time series approach to analyzing asset returns co-movements," Journal of Econometrics, Elsevier, vol. 229(1), pages 127-151.
    15. Wong, Raymond K.W. & Zhang, Xiaoke, 2019. "Nonparametric operator-regularized covariance function estimation for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 131-144.
    16. Yuan Wang & Jianhua Hu & Kim-Anh Do & Brian P. Hobbs, 2019. "An Efficient Nonparametric Estimate for Spatially Correlated Functional Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(1), pages 162-183, April.
    17. Chen, Xuerong & Li, Haoqi & Liang, Hua & Lin, Huazhen, 2019. "Functional response regression analysis," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 218-233.
    18. Wenjuan Hu & Nan Lin & Baoxue Zhang, 2020. "Nonparametric testing of lack of dependence in functional linear models," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-24, June.
    19. Seonjin Kim, 2015. "Hypothesis Testing For Arch Models: A Multiple Quantile Regressions Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 26-38, January.
    20. Li, Ting & Song, Xinyuan & Zhang, Yingying & Zhu, Hongtu & Zhu, Zhongyi, 2021. "Clusterwise functional linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).

    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:190:y:2022:i:c:s0047259x22000264. 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.