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One-Way anova for Functional Data via Globalizing the Pointwise F-test

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  • Jin-Ting Zhang
  • Xuehua Liang

Abstract

type="main" xml:id="sjos12025-abs-0001"> In this paper, we propose and study a new global test, namely, GPF test, for the one-way anova problem for functional data, obtained via globalizing the usual pointwise F-test. The asymptotic random expressions of the test statistic are derived, and its asymptotic power is investigated. The GPF test is shown to be root-n consistent. It is much less computationally intensive than a parametric bootstrap test proposed in the literature for the one-way anova for functional data. Via some simulation studies, it is found that in terms of size-controlling and power, the GPF test is comparable with two existing tests adopted for the one-way anova problem for functional data. A real data example illustrates the GPF test.

Suggested Citation

  • Jin-Ting Zhang & Xuehua Liang, 2014. "One-Way anova for Functional Data via Globalizing the Pointwise F-test," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 51-71, March.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:1:p:51-71
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    File URL: http://hdl.handle.net/10.1111/sjos.12025
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    References listed on IDEAS

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    1. Qiu, Zhiping & Chen, Jianwei & Zhang, Jin-Ting, 2021. "Two-sample tests for multivariate functional data with applications," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    2. Łukasz Smaga, 2020. "A note on repeated measures analysis for functional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 117-139, March.
    3. Zhu, Tianming & Zhang, Jin-Ting & Cheng, Ming-Yen, 2022. "One-way MANOVA for functional data via Lawley–Hotelling trace test," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    4. Huang, Wei-Hsueh & Huang, Li-Shan & Yang, Cheng-Tao, 2022. "Invariant tests for functional data with application to an earthquake impact study," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    5. Oomen, Roel, 2018. "Price signatures," LSE Research Online Documents on Economics 90481, London School of Economics and Political Science, LSE Library.
    6. Salamat Ullah & Arshad Jamal & Meshal Almoshaogeh & Fawaz Alharbi & Jawad Hussain, 2022. "Investigation of Resilience Characteristics of Unbound Granular Materials for Sustainable Pavements," Sustainability, MDPI, vol. 14(11), pages 1-20, June.
    7. Jiménez-Gamero, M. Dolores & Franco-Pereira, Alba M., 2021. "Testing the equality of a large number of means of functional data," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
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    10. Jing Zhao & Sanying Feng & Yuping Hu, 2022. "Two-Sample Hypothesis Test for Functional Data," Mathematics, MDPI, vol. 10(21), pages 1-16, November.
    11. Qiu, Zhiping & Fan, Jiangyuan & Zhang, Jin-Ting & Chen, Jianwei, 2024. "Tests for equality of several covariance matrix functions for multivariate functional data," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    12. Pini, Alessia & Sørensen, Helle & Tolver, Anders & Vantini, Simone, 2023. "Local inference for functional linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    13. Tianming Zhu, 2025. "The general linear hypothesis testing problem for multivariate functional data with applications," Statistical Papers, Springer, vol. 66(4), pages 1-32, June.
    14. Hlávka, Zdeněk & Hlubinka, Daniel & Koňasová, Kateřina, 2022. "Functional ANOVA based on empirical characteristic functionals," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    15. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
    16. Pini, Alessia & Spreafico, Lorenzo & Vantini, Simone & Vietti, Alessandro, 2019. "Multi-aspect local inference for functional data: Analysis of ultrasound tongue profiles," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 162-185.
    17. Tao Zhang & Zhiwen Wang & Yanling Wan, 2021. "Functional test for high-dimensional covariance matrix, with application to mitochondrial calcium concentration," Statistical Papers, Springer, vol. 62(3), pages 1213-1230, June.
    18. Hébert, Florian & Causeur, David & Emily, Mathieu, 2021. "An adaptive decorrelation procedure for signal detection," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    19. Tomasz Górecki & Łukasz Smaga, 2019. "fdANOVA: an R software package for analysis of variance for univariate and multivariate functional data," Computational Statistics, Springer, vol. 34(2), pages 571-597, June.
    20. Jie Li & Lintong Huang & Kai Zhu, 2023. "Ecological Health Assessment of an Urban River: The Case Study of Zhengzhou City, China," Sustainability, MDPI, vol. 15(10), pages 1-14, May.
    21. Tomasz Górecki & Łukasz Smaga, 2015. "A comparison of tests for the one-way ANOVA problem for functional data," Computational Statistics, Springer, vol. 30(4), pages 987-1010, December.
    22. González–Rodríguez, Gil & Colubi, Ana & González–Manteiga, Wenceslao & Febrero–Bande, Manuel, 2024. "A consistent test of equality of distributions for Hilbert-valued random elements," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    23. Rafael Meléndez & Ramón Giraldo & Víctor Leiva, 2020. "Sign, Wilcoxon and Mann-Whitney Tests for Functional Data: An Approach Based on Random Projections," Mathematics, MDPI, vol. 9(1), pages 1-11, December.

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