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Application of distance standard deviation in functional data analysis

Author

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  • Mirosław Krzyśko

    (Calisia University-Kalisz)

  • Łukasz Smaga

    (Adam Mickiewicz University)

Abstract

This paper concerns the measurement and testing of equality of variability of functional data. We apply the distance standard deviation constructed based on distance correlation, which was recently introduced as a measure of spread. For functional data, the distance standard deviation seems to measure different kinds of variability, not only scale differences. Moreover, the distance standard deviation is just one real number, and for this reason, it is of more practical value than the covariance function, which is a more difficult object to interpret. For testing equality of variability in two groups, we propose a permutation method based on centered observations, which controls the type I error level much better than the standard permutation method. We also consider the applicability of other correlations to measure the variability of functional data. The finite sample properties of two-sample tests are investigated in extensive simulation studies. We also illustrate their use in five real data examples based on various data sets.

Suggested Citation

  • Mirosław Krzyśko & Łukasz Smaga, 2024. "Application of distance standard deviation in functional data analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(2), pages 431-454, June.
    • Handle: RePEc:spr:advdac:v:18:y:2024:i:2:d:10.1007_s11634-023-00538-6
    DOI: 10.1007/s11634-023-00538-6
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    References listed on IDEAS

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    1. 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.
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    6. Jia Guo & Bu Zhou & Jin-Ting Zhang, 2019. "New Tests for Equality of Several Covariance Functions for Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1251-1263, July.
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