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Selected statistical methods of data analysis for multivariate functional data

Author

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  • Tomasz Górecki

    (Adam Mickiewicz University)

  • Mirosław Krzyśko

    (Adam Mickiewicz University)

  • Łukasz Waszak

    (Adam Mickiewicz University)

  • Waldemar Wołyński

    (Adam Mickiewicz University)

Abstract

Data in the form of a continuous vector function on a given interval are referred to as multivariate functional data. These data are treated as realizations of multivariate random processes. The paper is devoted to three statistical dimension reduction techniques for multivariate data. For the first one, principal components analysis, the authors present a review of a recent paper (Jacques and Preda in, Comput Stat Data Anal, 71:92–106, 2014). For two others one, canonical variables and discriminant coordinates, the authors extend existing works for univariate functional data to multivariate. These methods for multivariate functional data are presented, illustrated and discussed in the context of analyzing real data sets. Each of these techniques is applied on real data set.

Suggested Citation

  • Tomasz Górecki & Mirosław Krzyśko & Łukasz Waszak & Waldemar Wołyński, 2018. "Selected statistical methods of data analysis for multivariate functional data," Statistical Papers, Springer, vol. 59(1), pages 153-182, March.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0757-8
    DOI: 10.1007/s00362-016-0757-8
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    References listed on IDEAS

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    1. Krzyśko Miroslaw & Łukaszonek ojciech & Wolynski Waldemar, 2018. "Discriminant Coordinates Analysis In The Case Of Multivariate Repeated Measures Data," Statistics in Transition New Series, Polish Statistical Association, vol. 19(3), pages 495-506, September.
    2. Mirosław Krzyśko & Wojciech Łukaszonek & Waldemar Wołyński, 2018. "Discriminant Coordinates Analysis In The Case Of Multivariate Repeated Measures Data," Statistics in Transition New Series, Polish Statistical Association, vol. 19(3), pages 495-506, September.
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    4. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
    5. Aneiros, Germán & Horová, Ivana & Hušková, Marie & Vieu, Philippe, 2022. "On functional data analysis and related topics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    6. 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.
    7. Qiu, Zhiping & Chen, Jianwei & Zhang, Jin-Ting, 2021. "Two-sample tests for multivariate functional data with applications," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    8. B. Lafuente-Rego & P. D’Urso & J. A. Vilar, 2020. "Robust fuzzy clustering based on quantile autocovariances," Statistical Papers, Springer, vol. 61(6), pages 2393-2448, December.
    9. Tang Qingguo & Bian Minjie, 2021. "Estimation for functional linear semiparametric model," Statistical Papers, Springer, vol. 62(6), pages 2799-2823, December.
    10. Mirosław Krzyśko & Peter Nijkamp & Waldemar Ratajczak & Waldemar Wołyński, 2022. "Multidimensional economic indicators and multivariate functional principal component analysis (MFPCA) in a comparative study of countries’ competitiveness," Journal of Geographical Systems, Springer, vol. 24(1), pages 49-65, January.
    11. Mirosław Krzyśko & Waldemar Wołyńki & Marcin Szymkowiak & Andrzej Wojtyła, 2021. "A Spatio-Temporal Analysis of the Health Situation in Poland Based on Functional Discriminant Coordinates," IJERPH, MDPI, vol. 18(3), pages 1-17, January.
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    13. 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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