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Statistical Theory of Shape Under Elliptical Models via Polar Decompositions

Author

Listed:
  • José A. Daíz-García

    (Universidad Autónoma de Chihuahua)

  • Francisco J. Caro-Lopera

    (Universidad de Medellín)

Abstract

A new model of statistical shape theory under elliptical models is proposed by using the polar decomposition. This work completes the group of SVD and QR shape densities obtained from the transpose of the square root of a non singular Wishart matrix. The associated non isotropic and non central polar shape distributions are set in the context of consistent computable series of zonal polynomials. Then the inference procedures with elliptical assumptions can be performed at the same computational cost of the published routines based on Gaussian models. As an example of the technique, a classical application in Biology is studied under three models, the usual Gaussian and two Kotz type models; then the best model is selected by a modified BIC∗ criterion, and a test for equality in polar shapes is performed. The published results for this landmark data under isotropic Gaussian models and procrustes theory are also discussed.

Suggested Citation

  • José A. Daíz-García & Francisco J. Caro-Lopera, 2019. "Statistical Theory of Shape Under Elliptical Models via Polar Decompositions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 445-465, December.
    • Handle: RePEc:spr:sankha:v:81:y:2019:i:2:d:10.1007_s13171-018-0132-z
    DOI: 10.1007/s13171-018-0132-z
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    References listed on IDEAS

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    1. Díaz-García, José A. & Caro-Lopera, Francisco J., 2012. "Statistical theory of shape under elliptical models and singular value decompositions," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 77-92, January.
    2. Chih-Chien Yang & Chih-Chiang Yang, 2007. "Separating Latent Classes by Information Criteria," Journal of Classification, Springer;The Classification Society, vol. 24(2), pages 183-203, September.
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