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Statistical theory of shape under elliptical models and singular value decompositions

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  • Díaz-García, José A.
  • Caro-Lopera, Francisco J.

Abstract

The size-and-shape and shape distributions based on non-central and non-isotropic elliptical distributions are derived in this paper by using the singular value decomposition (SVD). The general densities require the computation of new integrals involving zonal polynomials. The invariance of the central shape distribution is also proved. Finally, some particular densities are applied in a classical data of Biology, and the inference based on exact distributions is performed after choosing the best model by using a modified BIC* criterion.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:103:y:2012:i:1:p:77-92
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. 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.
    2. Hong, Zhaoping & Lian, Heng, 2013. "Sparse-smooth regularized singular value decomposition," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 163-174.

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