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Two Sample Test for Extrinsic Antimeans on Kendall Planar Shape Spaces with Applications to Medical Imaging

Author

Listed:
  • Aaid Algahtani

    (King Saud University)

  • Vic Patrangenaru

    (Florida State University)

Abstract

This paper is specialized in deriving a large sample chi-square test for the equality of two extrinsic antimeans on a compact manifolds, using recent limit theorems for extrinsic sample antimeans relative to an arbitrary embedding of a such manifold into an Euclidean space. Applications are given to distributions on planar Kendall shape spaces, in their complex projective space representations, that are Veronese-Whitney embedded in spaces of self-adjoint matrices. Two medical imaging examples are also given.

Suggested Citation

  • Aaid Algahtani & Vic Patrangenaru, 2025. "Two Sample Test for Extrinsic Antimeans on Kendall Planar Shape Spaces with Applications to Medical Imaging," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 87(1), pages 96-113, February.
    • Handle: RePEc:spr:sankha:v:87:y:2025:i:1:d:10.1007_s13171-024-00365-7
    DOI: 10.1007/s13171-024-00365-7
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    References listed on IDEAS

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    1. R. N. Bhattacharya & L. Ellingson & X. Liu & V. Patrangenaru & M. Crane, 2012. "Extrinsic analysis on manifolds is computationally faster than intrinsic analysis with applications to quality control by machine vision," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(3), pages 222-235, May.
    2. Ruite Guo & Hwiyoung Lee & Vic Patrangenaru, 2023. "Test for Homogeneity of Random Objects on Manifolds with Applications to Biological Shape Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1178-1204, August.
    3. Wang, Yunfan & Patrangenaru, Vic & Guo, Ruite, 2020. "A Central Limit Theorem for extrinsic antimeans and estimation of Veronese–Whitney means and antimeans on planar Kendall shape spaces," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    4. Vic Patrangenaru & Yifang Deng, 2021. "Extrinsic Regression and Anti-Regression on Projective Shape Manifolds," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 629-646, June.
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