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Testing the Equality of Covariance Operators in Functional Samples

Author

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  • STEFAN FREMDT
  • JOSEF G. STEINEBACH
  • LAJOS HORVÁTH
  • PIOTR KOKOSZKA

Abstract

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Suggested Citation

  • Stefan Fremdt & Josef G. Steinebach & Lajos Horváth & Piotr Kokoszka, 2013. "Testing the Equality of Covariance Operators in Functional Samples," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 138-152, March.
    • Handle: RePEc:bla:scjsta:v:40:y:2013:i:1:p:138-152
    DOI: j.1467-9469.2012.00796.x
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    Citations

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    Cited by:

    1. Kathrin Bissantz & Nicolai Bissantz & Katharina Proksch, 2021. "Nonparametric detection of changes over time in image data from fluorescence microscopy of living cells," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 1001-1017, September.
    2. Ghiglietti, Andrea & Paganoni, Anna Maria, 2017. "Exact tests for the means of Gaussian stochastic processes," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 102-107.
    3. Ahmad, Rauf, 2022. "Tests for proportionality of matrices with large dimension," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    4. Boente, Graciela & Rodriguez, Daniela & Sued, Mariela, 2019. "The spatial sign covariance operator: Asymptotic results and applications," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 115-128.
    5. Tomasz Górecki & Lajos Horváth & Piotr Kokoszka, 2020. "Tests of Normality of Functional Data," International Statistical Review, International Statistical Institute, vol. 88(3), pages 677-697, December.
    6. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.
    7. 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.
    8. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
    9. Horváth, Lajos & Hušková, Marie & Rice, Gregory, 2013. "Test of independence for functional data," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 100-119.
    10. 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.
    11. 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.
    12. 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.
    13. R. Bárcenas & J. Ortega & A. J. Quiroz, 2017. "Quadratic forms of the empirical processes for the two-sample problem for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 503-526, September.
    14. Valentina Masarotto & Victor M. Panaretos & Yoav Zemel, 2019. "Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 172-213, February.
    15. 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.
    16. Hà Quang Minh, 2023. "Entropic Regularization of Wasserstein Distance Between Infinite-Dimensional Gaussian Measures and Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 36(1), pages 201-296, March.
    17. 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.
    18. Adam B. Kashlak & John A. D. Aston & Richard Nickl, 2019. "Inference on Covariance Operators via Concentration Inequalities: k-sample Tests, Classification, and Clustering via Rademacher Complexities," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 214-243, February.
    19. Kokoszka Piotr & Miao Hong & Zheng Ben, 2017. "Testing for asymmetry in betas of cumulative returns: Impact of the financial crisis and crude oil price," Statistics & Risk Modeling, De Gruyter, vol. 34(1-2), pages 33-53, June.
    20. 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.
    21. 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.
    22. 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.

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