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Pointwise testing with functional data using the Westfall--Young randomization method

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  • Dennis D. Cox
  • Jong Soo Lee

Abstract

We consider hypothesis testing with smooth functional data by performing pointwise tests and applying a multiple comparisons procedure. Methods based on general inequalities, such as Bonferroni's method, do not perform well because of the high correlation between observations at nearby points. We consider the multiple comparison procedure proposed by Westfall & Young (1993) and show that it approximates a multiple comparison correction for a continuum of comparisons as the grid for pointwise comparisons becomes finer. Simulations and an application verify that this result applies in practical settings. Copyright 2008, Oxford University Press.

Suggested Citation

  • Dennis D. Cox & Jong Soo Lee, 2008. "Pointwise testing with functional data using the Westfall--Young randomization method," Biometrika, Biometrika Trust, vol. 95(3), pages 621-634.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:3:p:621-634
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    File URL: http://hdl.handle.net/10.1093/biomet/asn021
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    Cited by:

    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. A. Pini & S. Vantini, 2017. "Interval-wise testing for functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 407-424, April.
    3. Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2018. "Hotelling’s T2 in separable Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 284-305.
    4. Zhang, Jin-Ting & Cheng, Ming-Yen & Wu, Hau-Tieng & Zhou, Bu, 2019. "A new test for functional one-way ANOVA with applications to ischemic heart screening," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 3-17.
    5. Ziegel, Johanna F. & Krueger, Fabian & Jordan, Alexander & Fasciati, Fernando, 2017. "Murphy Diagrams: Forecast Evaluation of Expected Shortfall," Working Papers 0632, University of Heidelberg, Department of Economics.
    6. 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).
    7. Vsevolozhskaya, O.A. & Greenwood, M.C. & Bellante, G.J. & Powell, S.L. & Lawrence, R.L. & Repasky, K.S., 2013. "Combining functions and the closure principle for performing follow-up tests in functional analysis of variance," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 175-184.
    8. Livio Corain & Viatcheslav Melas & Andrey Pepelyshev & Luigi Salmaso, 2014. "New insights on permutation approach for hypothesis testing on functional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 339-356, September.
    9. İstem Köymen Keser & İpek Deveci Kocakoç & Ali Kemal Şehirlioğlu, 2016. "A New Descriptive Statistic for Functional Data: Functional Coefficient of Variation," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 4(2), pages 1-10, September.
    10. 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.
    11. Konrad Abramowicz & Alessia Pini & Lina Schelin & Sara Sjöstedt de Luna & Aymeric Stamm & Simone Vantini, 2023. "Domain selection and familywise error rate for functional data: A unified framework," Biometrics, The International Biometric Society, vol. 79(2), pages 1119-1132, June.
    12. Jesse Hemerik & Jelle Goeman, 2018. "Exact testing with random permutations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 811-825, December.
    13. Johanna F. Ziegel & Fabian Kruger & Alexander Jordan & Fernando Fasciati, 2017. "Murphy Diagrams: Forecast Evaluation of Expected Shortfall," Papers 1705.04537, arXiv.org.

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