Statistical Theory of Shape Under Elliptical Models via Polar Decompositions

José A. daíz-García, Francisco J. Caro-Lopera

Resultado de la investigación: Contribución a una revistaArtículoInvestigaciónrevisión exhaustiva

Resumen

© 2018 Indian Statistical Institute 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.
Idioma originalInglés estadounidense
Páginas (desde-hasta)1-21
Número de páginas21
PublicaciónSankhya A
DOI
EstadoPublicada - 31 may 2018

Huella dactilar

Polar decomposition
Gaussian Model
Zonal Polynomials
Wishart Matrix
Singular matrix
Model
Transpose
Landmarks
Square root
Biology
Computational Cost
Equality
Decomposition
Series

Citar esto

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abstract = "{\circledC} 2018 Indian Statistical Institute 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.",
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Statistical Theory of Shape Under Elliptical Models via Polar Decompositions. / daíz-García, José A.; Caro-Lopera, Francisco J.

En: Sankhya A, 31.05.2018, p. 1-21.

Resultado de la investigación: Contribución a una revistaArtículoInvestigaciónrevisión exhaustiva

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