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A comparison of tests for the one-way ANOVA problem for functional data

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  • Tomasz Górecki
  • Łukasz Smaga

Abstract

In this paper, some new tests based on the idea of the B-spline test (Shen and Faraway in Stat Sin 14:1239–1257, 2004 ) for the one-way ANOVA problem for functional data are proposed. Eleven existing tests for this problem are also reviewed. Exhaustive simulation studies are presented to compare all of the tests considered. The simulations are based on real labeled times series data and artificial data. They provide an idea of the size control and power of the tests, and emphasize the differences between them. Illustrative examples of the use of the tests in practice are also given. Copyright The Author(s) 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:4:p:987-1010
    DOI: 10.1007/s00180-015-0555-0
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    1. 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.
    2. K. Benhenni & F. Ferraty & M. Rachdi & P. Vieu, 2007. "Local smoothing regression with functional data," Computational Statistics, Springer, vol. 22(3), pages 353-369, September.
    3. Martínez-Camblor, Pablo & Corral, Norberto, 2011. "Repeated measures analysis for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3244-3256, December.
    4. Berrendero, J.R. & Justel, A. & Svarc, M., 2011. "Principal components for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2619-2634, September.
    5. Cristian Preda & Gilbert Saporta & Caroline Lévéder, 2007. "PLS classification of functional data," Computational Statistics, Springer, vol. 22(2), pages 223-235, July.
    6. Chiou, Jeng-Min & Muller, Hans-Georg, 2007. "Diagnostics for functional regression via residual processes," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4849-4863, June.
    7. Laukaitis, Algirdas & Rackauskas, Alfredas, 2005. "Functional data analysis for clients segmentation tasks," European Journal of Operational Research, Elsevier, vol. 163(1), pages 210-216, May.
    8. Shuichi Tokushige & Hiroshi Yadohisa & Koichi Inada, 2007. "Crisp and fuzzy k-means clustering algorithms for multivariate functional data," Computational Statistics, Springer, vol. 22(1), pages 1-16, April.
    9. Mariano Valderrama, 2007. "An overview to modelling functional data," Computational Statistics, Springer, vol. 22(3), pages 331-334, September.
    10. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2004. "An anova test for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 111-122, August.
    11. Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
    12. Gareth M. James & Trevor J. Hastie, 2001. "Functional linear discriminant analysis for irregularly sampled curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 533-550.
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    4. Balogoun, Armando Sosthène Kali & Nkiet, Guy Martial & Ogouyandjou, Carlos, 2021. "Asymptotic normality of a generalized maximum mean discrepancy estimator," Statistics & Probability Letters, Elsevier, vol. 169(C).
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