Shape theory via polar decomposition

This work proposes a new model in the context of statistical theory of shape, based on the polar decomposition. The non isotropic noncentral elliptical shape distributions via polar decomposition is derived in the context of zonal polynomials, avoiding the invariant polynomials and the open problems for their computation. The new polar shape distributions are easily computable and then the inference procedure can be studied under exact densities. As an example of the technique, a classical application in Biology is studied under three models, the usual Gaussian and two non normal Kotz models; the best model is selected by a modified BIC criterion, then a test for equality in polar shapes is performed.Comment: 14 page

Shape Theory via QR decomposition

This work sets the non isotropic noncentral elliptical shape distributions via QR decomposition in the context of zonal polynomials, avoiding the invariant polynomials and the open problems for their computation. The new shape distributions are easily computable and then the inference procedure can be studied under exact densities instead under the published approximations and asymptotic densities under isotropic models. An application in Biology is studied under the classical gaussian approach and a two non gaussian models.Comment: 13 page