Statistical theory of shape under elliptical models and singular value decompositions
The authors deal with the development of theoretical results useful for studying singular value decompositions (SVDs). For deriving the size and shape distributions first they develop a pair of lemmata, to characterize the Jacobians of the decompositions and the joint density functions of (V,D). Then they are used for deriving the density of a cone and a disk. The study of the central cone and disk is developed. The results derived produced corollaries of the pervious theorems, where explicit expressions of the corresponding density functions are derived. They are given in terms of invariant polynomials The results are applied to well known data [\textit{K.V. Mardia} and \textit{I.L. Dryden}, Statistical shape analysis. Chichester: Wiley. (1998; Zbl 0901.62072)]. They develop explicit expressions of the disk density for the isotropic elliptic, Gaussian, and Kotz models K(3, 0,5) and K(2,0,5) for disks. They claim using numerical results that their proposal works better than the existent models based on previous theory.
non-central and non-isotropic shape densities
scientific article; zbMATH DE number 5963977
scientific article