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Classical testing in functional linear models

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  • Dehan Kong
  • Ana-Maria Staicu
  • Arnab Maity

Abstract

We extend four tests common in classical regression – Wald, score, likelihood ratio and F tests – to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:gnstxx:v:28:y:2016:i:4:p:813-838
    DOI: 10.1080/10485252.2016.1231806
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    Citations

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    Cited by:

    1. Xu, Jianjun & Cui, Wenquan, 2022. "A new RKHS-based global testing for functional linear model," Statistics & Probability Letters, Elsevier, vol. 182(C).
    2. Li, Meng & Wang, Kehui & Maity, Arnab & Staicu, Ana-Maria, 2022. "Inference in functional linear quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    3. 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.
    4. 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).
    5. 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.
    6. Meeks, Roland & Monti, Francesca, 2023. "Heterogeneous beliefs and the Phillips curve," Journal of Monetary Economics, Elsevier, vol. 139(C), pages 41-54.
    7. Petrovich, Justin & Reimherr, Matthew, 2017. "Asymptotic properties of principal component projections with repeated eigenvalues," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 42-48.
    8. 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.
    9. Jadhav, Sneha & Ma, Shuangge, 2021. "An association test for functional data based on Kendall’s Tau," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    10. 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.
    11. 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.
    12. Li, Ting & Song, Xinyuan & Zhang, Yingying & Zhu, Hongtu & Zhu, Zhongyi, 2021. "Clusterwise functional linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).

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