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New insights on permutation approach for hypothesis testing on functional data

Author

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  • Livio Corain
  • Viatcheslav Melas
  • Andrey Pepelyshev
  • Luigi Salmaso

Abstract

The permutation approach for testing the equality of distributions and thereby comparing two populations of functional data has recently received increasing attention thanks to the flexibility of permutation tests to handle complex testing problems. The purpose of this work is to present some new insights in the context of nonparametric inference on functional data using the permutation approach, more specifically we formally show the equivalence of some permutation procedures proposed in the literature and we suggest the use of the permutation and combination-based approach within the basis function approximation layout. Validation of theoretical results is shown by simulation studies. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Livio Corain & Viatcheslav Melas & Andrey Pepelyshev & Luigi Salmaso, 2014. "New insights on permutation approach for hypothesis testing on functional data," 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. 8(3), pages 339-356, September.
    • Handle: RePEc:spr:advdac:v:8:y:2014:i:3:p:339-356
    DOI: 10.1007/s11634-013-0162-2
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    References listed on IDEAS

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    1. Hervé Cardot & Luboš Prchal & Pascal Sarda, 2007. "No effect and lack-of-fit permutation tests for functional regression," Computational Statistics, Springer, vol. 22(3), pages 371-390, September.
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    6. Guanqun Cao & Lijian Yang & David Todem, 2012. "Simultaneous inference for the mean function based on dense functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 359-377.
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    Cited by:

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    3. Crawford, F. & Watling, D.P. & Connors, R.D., 2017. "A statistical method for estimating predictable differences between daily traffic flow profiles," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 196-213.
    4. Fabian J.E. Telschow & Michael R. Pierrynowski & Stephan F. Huckemann, 2021. "Functional inference on rotational curves under sample‐specific group actions and identification of human gait," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1256-1276, December.
    5. Konrad Abramowicz & Alessia Pini & Lina Schelin & Sara Sjöstedt de Luna & Aymeric Stamm & Simone Vantini, 2023. "Domain selection and familywise error rate for functional data: A unified framework," Biometrics, The International Biometric Society, vol. 79(2), pages 1119-1132, June.
    6. Pini, Alessia & Spreafico, Lorenzo & Vantini, Simone & Vietti, Alessandro, 2019. "Multi-aspect local inference for functional data: Analysis of ultrasound tongue profiles," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 162-185.
    7. Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2018. "Hotelling’s T2 in separable Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 284-305.
    8. Gina-Maria Pomann & Ana-Maria Staicu & Sujit Ghosh, 2016. "A two-sample distribution-free test for functional data with application to a diffusion tensor imaging study of multiple sclerosis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(3), pages 395-414, April.

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