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A Multi-Aspect Permutation Test for Goodness-of-Fit Problems

Author

Listed:
  • Rosa Arboretti

    (Department of Civil, Environmental and Architectural Engineering, University of Padova, 35131 Padova, Italy)

  • Elena Barzizza

    (Department of Management and Engineering, University of Padova, 36100 Vicenza, Italy)

  • Nicolò Biasetton

    (Department of Management and Engineering, University of Padova, 36100 Vicenza, Italy)

  • Riccardo Ceccato

    (Department of Management and Engineering, University of Padova, 36100 Vicenza, Italy)

  • Livio Corain

    (Department of Management and Engineering, University of Padova, 36100 Vicenza, Italy)

  • Luigi Salmaso

    (Department of Management and Engineering, University of Padova, 36100 Vicenza, Italy)

Abstract

Parametric techniques commonly rely on specific distributional assumptions. It is therefore fundamental to preliminarily identify the eventual violations of such assumptions. Therefore, appropriate testing procedures are required for this purpose to deal with a the goodness-of-fit (GoF) problem. This task can be quite challenging, especially with small sample sizes and multivariate data. Previous studiesshowed how a GoF problem can be easily represented through a traditional two-sample system of hypotheses. Following this idea, in this paper, we propose a multi-aspect permutation-based test to deal with the multivariate goodness-of-fit, taking advantage of the nonparametric combination (NPC) methodology. A simulation study is then conducted to evaluate the performance of our proposal and to identify the eventual critical scenarios. Finally, a real data application is considered.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:2:p:35-582:d:841510
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    References listed on IDEAS

    as
    1. Luigi Salmaso & Aldo Solari, 2005. "Multiple aspect testing for case-control designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(2), pages 331-340, November.
    2. 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.
    3. Brombin, Chiara & Salmaso, Luigi, 2009. "Multi-aspect permutation tests in shape analysis with small sample size," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3921-3931, October.
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