Statistical theory of shape under elliptical models and singular value decompositions

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

Resultado de la investigación: Contribución a una revistaArtículoInvestigaciónrevisión exhaustiva

4 Citas (Scopus)

Resumen

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. © 2011 Elsevier Inc.
Idioma originalInglés estadounidense
Páginas (desde-hasta)77-92
Número de páginas16
PublicaciónJournal of Multivariate Analysis
DOI
EstadoPublicada - 1 ene 2012

Huella dactilar

Singular value decomposition
Invariance
Polynomials
Zonal Polynomials
Elliptical Distribution
Exact Distribution
Biology
Model

Citar esto

@article{8bfeac49a3d64588b9a55f72e37c5ec2,
title = "Statistical theory of shape under elliptical models and singular value decompositions",
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. {\circledC} 2011 Elsevier Inc.",
author = "D{\'i}az-Garc{\'i}a, {Jos{\'e} A.} and Caro-Lopera, {Francisco J.}",
year = "2012",
month = "1",
day = "1",
doi = "10.1016/j.jmva.2011.06.010",
language = "American English",
pages = "77--92",
journal = "Journal of Multivariate Analysis",
issn = "0047-259X",
publisher = "Academic Press Inc.",

}

Statistical theory of shape under elliptical models and singular value decompositions. / Díaz-García, José A.; Caro-Lopera, Francisco J.

En: Journal of Multivariate Analysis, 01.01.2012, p. 77-92.

Resultado de la investigación: Contribución a una revistaArtículoInvestigaciónrevisión exhaustiva

TY - JOUR

T1 - Statistical theory of shape under elliptical models and singular value decompositions

AU - Díaz-García, José A.

AU - Caro-Lopera, Francisco J.

PY - 2012/1/1

Y1 - 2012/1/1

N2 - 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. © 2011 Elsevier Inc.

AB - 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. © 2011 Elsevier Inc.

U2 - 10.1016/j.jmva.2011.06.010

DO - 10.1016/j.jmva.2011.06.010

M3 - Article

SP - 77

EP - 92

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

ER -