IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v182y2022ics016771522100239x.html
   My bibliography  Save this article

A new RKHS-based global testing for functional linear model

Author

Listed:
  • Xu, Jianjun
  • Cui, Wenquan

Abstract

This article studies global testing of the slope function in the functional linear regression model in the framework of reproducing kernel Hilbert space. We propose a new testing statistic based on smoothness regularization estimators. The asymptotic distribution of the testing statistic is established under the null hypothesis. It is shown that the null asymptotic distribution is determined jointly by the reproducing kernel and the covariance function of the covariate. Our theoretical analysis shows that the proposed testing is consistent over a class of smooth local alternatives. Despite the generality of the method of regularization, we show the procedure is easily implementable. Numerical examples are provided to demonstrate the empirical advantages over the competing methods.

Suggested Citation

  • Xu, Jianjun & Cui, Wenquan, 2022. "A new RKHS-based global testing for functional linear model," Statistics & Probability Letters, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:stapro:v:182:y:2022:i:c:s016771522100239x
    DOI: 10.1016/j.spl.2021.109277
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771522100239X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2021.109277?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. Hervé Cardot & Frédéric Ferraty & André Mas & Pascal Sarda, 2003. "Testing Hypotheses in the Functional Linear Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 241-255, March.
    2. 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.
    3. 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.
    4. Zhenhua Lin & Fang Yao, 2021. "Functional regression on the manifold with contamination," Biometrika, Biometrika Trust, vol. 108(1), pages 167-181.
    5. 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.
    6. 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.
    7. Jing Lei, 2014. "Adaptive Global Testing for Functional Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 624-634, 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. Jadhav, Sneha & Ma, Shuangge, 2021. "An association test for functional data based on Kendall’s Tau," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    2. 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.
    3. Li, Meng & Wang, Kehui & Maity, Arnab & Staicu, Ana-Maria, 2022. "Inference in functional linear quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    4. Merve Yasemin Tekbudak & Marcela Alfaro-Córdoba & Arnab Maity & Ana-Maria Staicu, 2019. "A comparison of testing methods in scalar-on-function regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 411-436, September.
    5. 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.
    6. 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.
    7. 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.
    8. Zhang, Xiaochen & Zhang, Qingzhao & Ma, Shuangge & Fang, Kuangnan, 2022. "Subgroup analysis for high-dimensional functional regression," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    9. Shuzhi Zhu & Peixin Zhao, 2019. "Tests for the linear hypothesis in semi-functional partial linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 125-148, March.
    10. Eduardo García‐Portugués & Javier Álvarez‐Liébana & Gonzalo Álvarez‐Pérez & Wenceslao González‐Manteiga, 2021. "A goodness‐of‐fit test for the functional linear model with functional response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 502-528, June.
    11. 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.
    12. Chiou, Jeng-Min & Muller, Hans-Georg, 2007. "Diagnostics for functional regression via residual processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4849-4863, June.
    13. Li, Ting & Song, Xinyuan & Zhang, Yingying & Zhu, Hongtu & Zhu, Zhongyi, 2021. "Clusterwise functional linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    14. Wu Wang & Ying Sun & Huixia Judy Wang, 2023. "Latent group detection in functional partially linear regression models," Biometrics, The International Biometric Society, vol. 79(1), pages 280-291, March.
    15. Zhang, Tao & Zhang, Qingzhao & Wang, Qihua, 2014. "Model detection for functional polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 183-197.
    16. 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.
    17. Jingjing Yang & Dennis D. Cox & Jong Soo Lee & Peng Ren & Taeryon Choi, 2017. "Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian–Wishart processes," Biometrics, The International Biometric Society, vol. 73(4), pages 1082-1091, December.
    18. Liu, Yuzi & Peng, Ling & Liu, Qing & Lian, Heng & Liu, Xiaohui, 2023. "Functional additive expectile regression in the reproducing kernel Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    19. 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.
    20. 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.

    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:stapro:v:182:y:2022:i:c:s016771522100239x. 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.