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Finite-sample consistency of combination-based permutation tests with application to repeated measures designs

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  • Fortunato Pesarin
  • Luigi Salmaso

Abstract

In several application fields, e.g. genetics, image and functional analysis, several biomedical and social experimental and observational studies, etc. it may happen that the number of observed variables is much larger than that of subjects. It can be proved that, for a given and fixed number of subjects, when the number of variables increases and the noncentrality parameter of the underlying population distribution increases with respect to each added variable, then power of multivariate permutation tests based on Pesarin's combining functions [Pesarin, F. (2001), Multivariate Permutation Tests with Applications in Biostatistics, New York: Wiley, Chichester] is monotonically increasing. These results confirm and extend those presented by [Blair, Higgins, Karniski and Kromrey (1994), ‘A Study of Multivariate Permutation Tests which May Replace Hotelling's T2 Test in Prescribed Circumstances’, Multivariate Behavioral Research 29, 141–163]. Moreover, they allow us to introduce the property of finite-sample consistency for those kinds of combination-based permutation tests. Sufficient conditions are given in order that the rejection rate converges to one, for fixed sample sizes at any attainable α -values, when the number of variables diverges. A simulation study and a real case study are presented.

Suggested Citation

  • Fortunato Pesarin & Luigi Salmaso, 2010. "Finite-sample consistency of combination-based permutation tests with application to repeated measures designs," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 669-684.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:669-684
    DOI: 10.1080/10485250902807407
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    Cited by:

    1. Jung, Sungkyu & Sen, Arusharka & Marron, J.S., 2012. "Boundary behavior in High Dimension, Low Sample Size asymptotics of PCA," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 190-203.
    2. Härdle, Wolfgang Karl & Ritov, Ya’acov & Wang, Weining, 2015. "Tie the straps: Uniform bootstrap confidence bands for semiparametric additive models," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 129-145.
    3. Friedrich, Sarah & Brunner, Edgar & Pauly, Markus, 2017. "Permuting longitudinal data in spite of the dependencies," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 255-265.
    4. Jesse Hemerik & Jelle J. Goeman & Livio Finos, 2020. "Robust testing in generalized linear models by sign flipping score contributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 841-864, July.
    5. Arboretti, Rosa & Bonnini, Stefano & Corain, Livio & Salmaso, Luigi, 2014. "A permutation approach for ranking of multivariate populations," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 39-57.
    6. Elena Barzizza & Nicolò Biasetton & Riccardo Ceccato & Luigi Salmaso, 2023. "Big Data Analytics and Machine Learning in Supply Chain 4.0: A Literature Review," Stats, MDPI, vol. 6(2), pages 1-21, May.
    7. Stefano Bonnini & Michela Borghesi, 2022. "Relationship between Mental Health and Socio-Economic, Demographic and Environmental Factors in the COVID-19 Lockdown Period—A Multivariate Regression Analysis," Mathematics, MDPI, vol. 10(18), pages 1-15, September.
    8. Rosa Arboretti & Elena Barzizza & Nicolò Biasetton & Riccardo Ceccato & Livio Corain & Luigi Salmaso, 2022. "A Multi-Aspect Permutation Test for Goodness-of-Fit Problems," Stats, MDPI, vol. 5(2), pages 1-11, June.
    9. Chiara Brombin & Luigi Salmaso & Lara Fontanella & Luigi Ippoliti, 2015. "Nonparametric combination-based tests in dynamic shape analysis," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(4), pages 460-484, December.

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