Statistical theory of shape under elliptical models and singular value decompositions

José A. Díaz-García and Francisco J. Caro-Lopera

Journal of Multivariate Analysis, 2012, vol. 103, issue 1, 77-92

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.

Keywords: Shape; theory; Non-central; and; non-isotropic; shape; density; Zonal; polynomials; Singular; value; decomposition; Maximum; likelihood; estimators (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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