Statistical Theory of Shape Under Elliptical Models via Polar Decompositions

José A. Daíz-García () and Francisco J. Caro-Lopera ()
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José A. Daíz-García: Universidad Autónoma de Chihuahua
Francisco J. Caro-Lopera: Universidad de Medellín

Sankhya A: The Indian Journal of Statistics, 2019, vol. 81, issue 2, No 8, 445-465

Abstract: 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.

Keywords: Wishart type distributions; Shape theory; Non-central and non-isotropic shape density; Maximum likelihood estimators; Zonal polynomials; Polar decomposition.; Primary: 60E05; Secondary: 62E15; 62H99 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13171-018-0132-z

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