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Bootstrap-based testing of equality of mean functions or equality of covariance operators for functional data

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  • E. Paparoditis
  • T. Sapatinas

Abstract

We investigate the properties of a simple bootstrap method for testing the equality of mean functions or of covariance operators in functional data. Theoretical size and power results are derived for certain test statistics, whose limiting distributions depend on unknown infinite-dimensional parameters. Simulations demonstrate good size and power of the bootstrap-based functional tests.

Suggested Citation

  • E. Paparoditis & T. Sapatinas, 2016. "Bootstrap-based testing of equality of mean functions or equality of covariance operators for functional data," Biometrika, Biometrika Trust, vol. 103(3), pages 727-733.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:3:p:727-733.
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    File URL: http://hdl.handle.net/10.1093/biomet/asw033
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    Cited by:

    1. Guo, Jia & Zhou, Bu & Zhang, Jin-Ting, 2018. "Testing the equality of several covariance functions for functional data: A supremum-norm based test," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 15-26.
    2. Leucht, Anne & Paparoditis, Efstathios & Rademacher, Daniel & Sapatinas, Theofanis, 2022. "Testing equality of spectral density operators for functional processes," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Graciela Boente & Daniela Rodriguez & Mariela Sued, 2018. "Testing equality between several populations covariance operators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 919-950, August.
    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. Chen, Yichao & Pun, Chi Seng, 2019. "A bootstrap-based KPSS test for functional time series," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    6. Hlávka, Zdeněk & Hlubinka, Daniel & Koňasová, Kateřina, 2022. "Functional ANOVA based on empirical characteristic functionals," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    7. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
    8. Jia Guo & Bu Zhou & Jianwei Chen & Jin-Ting Zhang, 2019. "An $${{\varvec{L}}}^{2}$$L2-norm-based test for equality of several covariance functions: a further study," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1092-1112, December.
    9. Holger Dette & Kevin Kokot, 2022. "Detecting relevant differences in the covariance operators of functional time series: a sup-norm approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 195-231, April.
    10. Alexander S. Long & Brian J. Reich & Ana‐Maria Staicu & John Meitzen, 2023. "A nonparametric test of group distributional differences for hierarchically clustered functional data," Biometrics, The International Biometric Society, vol. 79(4), pages 3778-3791, December.
    11. 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).
    12. Dimitrios Pilavakis & Efstathios Paparoditis & Theofanis Sapatinas, 2020. "Testing equality of autocovariance operators for functional time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 571-589, July.
    13. 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).
    14. Chaouch, Mohamed, 2019. "Volatility estimation in a nonlinear heteroscedastic functional regression model with martingale difference errors," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 129-148.
    15. Holger Dette & Kevin Kokot & Stanislav Volgushev, 2020. "Testing relevant hypotheses in functional time series via self‐normalization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 629-660, July.

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