Statistical theory of shape under elliptical models and singular value decompositions

详细信息    查看全文

• 作者：José ; A. D&#xed ; az-Garc&#xed ; a^a ; ^{jadiaz@uaaan.mx"" rel=""nofollow} ; ^{jadiazg@ugr.es"" rel=""nofollow} ; Francisco J. Caro-Lopera^b ; ^{fjcaro@udem.edu.co"" rel=""nofollow}
• 关键词：Shape theory ; Non-central and non-isotropic shape density ; Zonal polynomials ; Singular value decomposition ; Maximum likelihood estimators
• 刊名：Journal of Multivariate Analysis
• 出版年：2012
• 出版时间：January 2012
• 年：2012
• 卷：103
• 期：1
• 页码：77-92
• 全文大小：430 K

文摘

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.