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Modeling shape distributions and inferences for assessing differences in shapes

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  • Micheas, Athanasios C.
  • Dey, Dipak K.

Abstract

The general class of complex elliptical shape distributions on a complex sphere provides a natural framework for modeling shapes in two dimensions. Such class includes many distributions, e.g., complex Normal, Watson, Bingham, angular central Gaussian and several others. We employ this class of distributions to develop methods for asserting differences in populations of shapes in two dimensions. Maximum likelihood and Bayesian methods for estimation of modal difference are developed along with hypothesis testing and credible regions for average shape difference. The methodology is applied in an example from biometry, where we are interested in detecting shape differences between male and female gorilla skulls.

Suggested Citation

  • Micheas, Athanasios C. & Dey, Dipak K., 2005. "Modeling shape distributions and inferences for assessing differences in shapes," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 257-280, February.
    • Handle: RePEc:eee:jmvana:v:92:y:2005:i:2:p:257-280
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    References listed on IDEAS

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    1. Sutradhar, Brajendra C. & Ali, Mir M., 1989. "A generalization of the Wishart distribution for the elliptical model and its moments for the multivariate t model," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 155-162, April.
    2. K. V. Mardia & I. L. Dryden, 1999. "The complex Watson distribution and shape analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 913-926.
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    Cited by:

    1. H. Fotouhi & M. Golalizadeh, 2015. "Highly resistant gradient descent algorithm for computing intrinsic mean shape on similarity shape spaces," Statistical Papers, Springer, vol. 56(2), pages 391-410, May.
    2. Valdevino Félix de Lima, Wenia & David Costa do Nascimento, Abraão & José Amorim do Amaral, Getúlio, 2021. "Distance-based tests for planar shape," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    3. Athanasios Micheas & Yuqiang Peng, 2010. "Bayesian Procrustes analysis with applications to hydrology," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(1), pages 41-55.
    4. 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.
    5. Alshabani, A.K.S. & Dryden, I.L. & Litton, C.D., 2007. "Partial size-and-shape distributions," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1988-2001, November.

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