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Multivariate analysis of variance for functional data

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  • T. Górecki
  • Ł. Smaga

Abstract

Functional data are being observed frequently in many scientific fields, and therefore most of the standard statistical methods are being adapted for functional data. The multivariate analysis of variance problem for functional data is considered. It seems to be of practical interest similarly as the one-way analysis of variance for such data. For the MANOVA problem for multivariate functional data, we propose permutation tests based on a basis function representation and tests based on random projections. Their performance is examined in comprehensive simulation studies, which provide an idea of the size control and power of the tests and identify differences between them. The simulation experiments are based on artificial data and real labeled multivariate time series data found in the literature. The results suggest that the studied testing procedures can detect small differences between vectors of curves even with small sample sizes. Illustrative real data examples of the use of the proposed testing procedures in practice are also presented.

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  • T. Górecki & Ł. Smaga, 2017. "Multivariate analysis of variance for functional data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2172-2189, September.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:12:p:2172-2189
    DOI: 10.1080/02664763.2016.1247791
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    1. Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef, 2007. "On sequential detection of parameter changes in linear regression," Statistics & Probability Letters, Elsevier, vol. 77(9), pages 885-895, May.
    2. Carlo Sguera & Pedro Galeano & Rosa Lillo, 2014. "Spatial depth-based classification for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 725-750, December.
    3. 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.
    4. Gregorutti, Baptiste & Michel, Bertrand & Saint-Pierre, Philippe, 2015. "Grouped variable importance with random forests and application to multiple functional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 15-35.
    5. Cuesta-Albertos, J.A. & del Barrio, E. & Fraiman, R. & Matran, C., 2007. "The random projection method in goodness of fit for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4814-4831, June.
    6. 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.
    7. Martínez-Camblor, Pablo & Corral, Norberto, 2011. "Repeated measures analysis for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3244-3256, December.
    8. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    9. 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.
    10. Boente, Graciela & Salibián Barrera, Matías & Tyler, David E., 2014. "A characterization of elliptical distributions and some optimality properties of principal components for functional data," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 254-264.
    11. Guo, Mengmeng & Zhou, Lhan & Huang, Jianhua Z. & Härdle, Wolfgang Karl, 2013. "Functional data analysis of generalized quantile regressions," SFB 649 Discussion Papers 2013-001, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    12. Manteiga, Wenceslao Gonzalez & Vieu, Philippe, 2007. "Statistics for Functional Data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4788-4792, June.
    13. Istem Koymen Keser & Ipek Deveci Kocako�, 2015. "Smoothed functional canonical correlation analysis of humidity and temperature data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2126-2140, October.
    14. 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.
    15. Schott, James R., 2007. "Some high-dimensional tests for a one-way MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1825-1839, October.
    16. 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.
    17. Fremdt, Stefan & Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef G., 2014. "Functional data analysis with increasing number of projections," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 313-332.
    18. Jaromir Antoch & Lubos Prchal & Maria Rosaria De Rosa & Pascal Sarda, 2010. "Electricity consumption prediction with functional linear regression using spline estimators," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(12), pages 2027-2041.
    19. J. Cuesta-Albertos & M. Febrero-Bande, 2010. "A simple multiway ANOVA for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 537-557, November.
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    Cited by:

    1. Mirosław Krzyśko & Łukasz Smaga, 2017. "An Application Of Functional Multivariate Regression Model To Multiclass Classification," Statistics in Transition New Series, Polish Statistical Association, vol. 18(3), pages 433-442, September.
    2. Kyunghee Han & Pantelis Z Hadjipantelis & Jane-Ling Wang & Michael S Kramer & Seungmi Yang & Richard M Martin & Hans-Georg Müller, 2018. "Functional principal component analysis for identifying multivariate patterns and archetypes of growth, and their association with long-term cognitive development," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-18, November.
    3. 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.
    4. Zhuo Qu & Wenlin Dai & Marc G. Genton, 2021. "Robust functional multivariate analysis of variance with environmental applications," Environmetrics, John Wiley & Sons, Ltd., vol. 32(1), February.

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