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fdANOVA: an R software package for analysis of variance for univariate and multivariate functional data

Author

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  • Tomasz Górecki

    (Adam Mickiewicz University)

  • Łukasz Smaga

    (Adam Mickiewicz University)

Abstract

Functional data, i.e., observations represented by curves or functions, frequently arise in various fields. The theory and practice of statistical methods for such data is referred to as functional data analysis (FDA) which is one of major research fields in statistics. The practical use of FDA methods is made possible thanks to availability of specialized and usually free software. In particular, a number of R packages is devoted to these methods. In the paper, we introduce a new R package fdANOVA which provides an access to a broad range of global analysis of variance methods for univariate and multivariate functional data. The implemented testing procedures mainly for homoscedastic case are briefly overviewed and illustrated by examples on a well known functional data set. To reduce the computation time, parallel implementation is developed and its efficiency is empirically evaluated. Since some of the implemented tests have not been compared in terms of size control and power yet, appropriate simulations are also conducted. Their results can help in choosing proper testing procedures in practice.

Suggested Citation

  • Tomasz Górecki & Łukasz Smaga, 2019. "fdANOVA: an R software package for analysis of variance for univariate and multivariate functional data," Computational Statistics, Springer, vol. 34(2), pages 571-597, June.
  • Handle: RePEc:spr:compst:v:34:y:2019:i:2:d:10.1007_s00180-018-0842-7
    DOI: 10.1007/s00180-018-0842-7
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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. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
    3. Markus Pauly & Edgar Brunner & Frank Konietschke, 2015. "Asymptotic permutation tests in general factorial designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 461-473, March.
    4. Paweł Teisseyre & Robert A. Kłopotek & Jan Mielniczuk, 2016. "Random Subspace Method for high-dimensional regression with the R package regRSM," Computational Statistics, Springer, vol. 31(3), pages 943-972, September.
    5. 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.
    6. Schmidberger, Markus & Morgan, Martin & Eddelbuettel, Dirk & Yu, Hao & Tierney, Luke & Mansmann, Ulrich, 2009. "State of the Art in Parallel Computing with R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i01).
    7. 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.
    8. 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:

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    3. Hlávka, Zdeněk & Hlubinka, Daniel & Koňasová, Kateřina, 2022. "Functional ANOVA based on empirical characteristic functionals," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
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    5. Germán Aneiros & Ricardo Cao & Philippe Vieu, 2019. "Editorial on the special issue on Functional Data Analysis and Related Topics," Computational Statistics, Springer, vol. 34(2), pages 447-450, June.
    6. 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).
    7. 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).
    8. Ofélia Anjos & Miguel Martínez Comesaña & Ilda Caldeira & Soraia Inês Pedro & Pablo Eguía Oller & Sara Canas, 2020. "Application of Functional Data Analysis and FTIR-ATR Spectroscopy to Discriminate Wine Spirits Ageing Technologies," Mathematics, MDPI, vol. 8(6), pages 1-21, June.
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    10. Rafael Meléndez & Ramón Giraldo & Víctor Leiva, 2020. "Sign, Wilcoxon and Mann-Whitney Tests for Functional Data: An Approach Based on Random Projections," Mathematics, MDPI, vol. 9(1), pages 1-11, December.

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