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Permutation testing for thick data when the number of variables is much greater than the sample size: recent developments and some recommendations

Author

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  • Patrick B. Langthaler

    (University of Salzburg
    Paracelsus Medical University)

  • Riccardo Ceccato

    (University of Padova)

  • Luigi Salmaso

    (University of Padova)

  • Rosa Arboretti

    (University of Padova)

  • Arne C. Bathke

    (Paracelsus Medical University
    University of Salzburg)

Abstract

In many scientific disciplines datasets contain many more variables than observational units (so-called thick data). A common hypothesis of interest in this setting is the global null hypothesis of no difference in multivariate distribution between different experimental or observational groups. Several permutation-based nonparametric tests have been proposed for this hypothesis. In this paper we investigate the potential differences in performance between different methods used to test thick data. In particular we focus on an extension of the Nonparametric combination procedure (NPC) proposed by Pesarin and Salmaso, a rank-based approach by Ellis, Burchett, Harrar and Bathke, and a distance-based approach by Mielke. The effect of different combining procedures on the NPC is also explored. Finally, we illustrate the use of these methods on a real-life dataset.

Suggested Citation

  • Patrick B. Langthaler & Riccardo Ceccato & Luigi Salmaso & Rosa Arboretti & Arne C. Bathke, 2023. "Permutation testing for thick data when the number of variables is much greater than the sample size: recent developments and some recommendations," Computational Statistics, Springer, vol. 38(1), pages 101-132, March.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:1:d:10.1007_s00180-022-01218-3
    DOI: 10.1007/s00180-022-01218-3
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    References listed on IDEAS

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    1. François Baccelli & Armand M. Makowski, 1989. "Multidimensional Stochastic Ordering and Associated Random Variables," Operations Research, INFORMS, vol. 37(3), pages 478-487, June.
    2. Bathke, Arne C. & Harrar, Solomon W. & Madden, Laurence V., 2008. "How to compare small multivariate samples using nonparametric tests," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4951-4965, July.
    3. N A Heard & P Rubin-Delanchy, 2018. "Choosing between methods of combining $p$-values," Biometrika, Biometrika Trust, vol. 105(1), pages 239-246.
    4. Burchett, Woodrow W. & Ellis, Amanda R. & Harrar, Solomon W. & Bathke, Arne C., 2017. "Nonparametric Inference for Multivariate Data: The R Package npmv," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i04).
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