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Multi-aspect permutation tests in shape analysis with small sample size

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  • Brombin, Chiara
  • Salmaso, Luigi

Abstract

Inferential methods known in the shape analysis literature make use of configurations of landmarks optimally superimposed using a least-squares procedure or analyze matrices of interlandmark distances. For example, in the two independent sample case, a practical method for comparing the mean shapes in the two groups is to use the Procrustes tangent space coordinates, if data are concentrated, calculate the Mahalanobis distance and then the Hotelling T2-test statistic. Under the assumption of isotropy, another simple approach is to work with statistics based on the squared Procrustes distance and then consider the Goodall F-test statistic. Despite their widespread use, on the one hand it is well known that Hotelling's T2-test may not be very powerful unless there are a large number of observations available, and on the other hand the underlying model required by Goodall's F-test is very restrictive. For these reasons, an extension of the nonparametric combination (NPC) methodology to shape analysis is proposed. Focussing on the two independent sample case, through a comparative simulation study and an application to the Mediterranean monk seal skulls dataset, the behaviour of some nonparametric permutation tests has been evaluated, showing that the proposed tests are very powerful, for both balanced and unbalanced sample sizes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:3921-3931
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    References listed on IDEAS

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    1. Salmaso, Luigi & Solari, Aldo, 2006. "Nonparametric iterated combined tests for genetic differentiation," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 1105-1112, February.
    2. Amaral, G.J.A. & Dryden, I.L. & Wood, Andrew T.A., 2007. "Pivotal Bootstrap Methods for k-Sample Problems in Directional Statistics and Shape Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 695-707, June.
    3. 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.
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    1. Stefano Bonnini & Getnet Melak Assegie & Kamila Trzcinska, 2024. "Review about the Permutation Approach in Hypothesis Testing," Mathematics, MDPI, vol. 12(17), pages 1-29, August.
    2. 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.
    3. Kherad-Pajouh, Sara & Renaud, Olivier, 2010. "An exact permutation method for testing any effect in balanced and unbalanced fixed effect ANOVA," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1881-1893, July.
    4. 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.
    5. Lovato, Ilenia & Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2020. "Model-free two-sample test for network-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    6. Hui, Francis K.C. & Geenens, Gery, 2012. "Nonparametric bootstrap tests of conditional independence in two-way contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 130-144.
    7. 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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